function f(x) = x'-0,2·x² +x. X 0,7 0,8 0,9 1,0 1,1 f(x) 0,945 1,184 1,467 1,800 2,189 a) From the above data set, find the numerical derivative values of f"(0,75)and f"(1,1) with finite difference method

function f(x) = x'-0,2·x² +x. X 0,7 0,8 0,9 1,0 1,1 f(x) 0,945 1,184 1,467 1,800 2,189 a) From the above data set, find the numerical derivative values of f"(0,75)and f"(1,1) with finite difference method

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 3E

See similar textbooks

Related questions

Q: Derivative of f(x)=1+ 2x+3xy computed * O explicitly equal to 2+3x implicitly equal to 2+3x+3dy/dx O…

Q: Derivative of In |x| Differentiate In x, for x > 0, and differentiate In(-x), for x < 0, to conclude…

Q: function of the radius (r) and the height (h) and is given by V= pi r2h. Determine the two parital…

Q: Use forward, backward and centered difference approximations to estimate the first derivative of:…

Q: Using the fact that Inſu(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the…

A: Given: lnuxvx=ln ux+ln vx

Q: The method of u-substitution is the integral analog of the chain rule of derivatives and the method…

A: Let say we have two functions f(x) & g(x)Now combine the function f(g(x))Hence, the derivative…

Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

Q: tionship between x and y.

A: Linear Eq: 9.x=1,2,3,4,5y=f(x)=2,4,6,8,102y=xSo, this is the requiredequation of line.

Q: Partial Differentiation. If u = In(x² + y²) and z = sin-1 *(÷), evaluat-

A: Differentiate the following

Q: Find the critical point of the function. Then use the second derivative test to classify the nature…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Consider the function f(x,y)= 2-x* +2x² – y² Find the critical points of f. Use the second…

A: At first we calculate D=fxxfyy-fxy2 at each critical points. If D<0 the critical point is a…

Q: 1. Centered-difference formula for the second derivative with one independent variable x y (x + h) –…

A: Claim: y''(x) = y(x+h)-2y(x)+y(x-h)h2-h212y(4)(ς) It is known that y = (x-∆x) =y(x) -∆xy'(x)…

Q: Compute the required derivative approximations for the functions at the specified location, for the…

Q: Find a function

A: This is very intresting question because there are so many function on an interval whose first…

Q: Differentiate Derivative of Derivative Differentiation Outer of Inner Function Function 1. y =…

Q: Test for homogeneity f(x,y)=tanx-sec2x-cosy

Q: In cubic spline interpolation, † the first and the second derivatives of the spline is continuous at…

A: CUBIC SPLINE:- C2-continuous pi(t)=ait3+bit2+cit+di now the solution of the given…

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: sinx 2x-x-1…

Q: Find the numerical second derivative value f''(0.5) from the data set using the finite difference…

A: given the function is f(x)=x3+0.4x2+x find the derivative f'(x)=3x2+0.8x+1 again find the second…

Q: In(cos(x)) cos(In(x)) Find the derivative of cos(In(x)) – In(cos(x)) sin(In(x)) A cos (In(x)) -xcos…

Q: Calculate the derivatives of all orders: f '(x), f ''(x), f '''(x), f (4)(x), , f (n)(x), f(x)…

Q: f(x)=sinh(x)+2cosh(x)-sech(x) O f(x)=cosh(x)+2sinh(x)-sech(x)tanh(x) O…

Q: Calculate the partial derivative using implicit differentiation of + = 10 at (x, y, w) = (1,2, 1).…

A: Given query is to find the derivative of the expression.

Q: Compute for the derivative of the function using rules for differentiation. Properly implement the…

Q: 0,2 0,3 0,4 0,5 0,6 X f(x) 0,224 0,363 0,528 0,725 0,960

Q: This is determined by the largest derivative, or the highest level of differentiation, present in a…

A: We have to check

Q: total derivative of the function f(x, y

Q: Calculate first, second, and third derivative values for function, f(x)=x² + 5x +3 oints x-2,0,2…

A: Forward differenceConsider a linear interpolation between the current data value (t0,I0) and the…

Q: derivative of y with respect to x. y= In (6 In x) dy dx %3D

Q: Find the critical point(s) of the function f (x, y) = xy + ln x + 2y . Then use the second…

A: Find critical points, nature of critical points and relative extrema of the given function.

Q: 9 f:(-0,0) U (0, ∞) → (∞,0) U (0, ∞0). Where f(x) х Show that f(x) is continuous at x=3 with the…

Q: True or false The slope of th tangent line to a dfferentiable function f at the point (2,f(x)) is

A: The slope of the tangent line to a differentiable function f at the point (2, f(x)) is

Q: ctivity 1. Find the 2nd derivative of the even-numbered functions ar dd-numbered ones: 1. f(x) = (x…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Are there independent linear functions with derivative number n – 1 continuous 91 ,..., „,with…

Q: Using the fact that In[u(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the…

A: Given: lnuxvx=lnux+lnvxddxlnx=1x

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: The given function is fx=2x2+5. The average rate of change of a function f over the interval x,x+h…

Q: Calculate the derivatives of all orders: f '(x), f ''(x), f '''(x), f (4)(x), , f (n)(x), f(x)…

Q: 1. f(x) = sin x at the point with abscissa x = A. Point of Tangency B. The Gradient of the Tangent…

A: Equation of tangent and normal

Q: 1. Use centered-difference approximation to estimate the first and second derivatives of y = xex at…

A: Given function is y=f(x)=xexx+1 and h=0.1 O(h2) formulae f'(x)=f(x+h)-f(x-h)2h…

Q: 11) The derivative of a function x f(x) MEGSures a) the areas under or between curves

A: In the given question, concept of derivative is applied. Derivative The derivative expresses the…

Q: Suppose the derivative of the function y = f(x) is y = x!/5(x +5). Determine the intervals on which…

A: Given y=fxy'=x15x+5 To find intervals in which f(x) is increasing and decreasing

Q: Find the critical points of the function f(x,y) = x^4 + y^4 - 196xy and use the Second Derivative…

Q: E- {\,23, X= {1,2,3, 48 T= {0,213,254} find the fallowing:- 1- The goroup derivative dE), Do you (E)…

A: Given that E=1,2 and τ=∅,1,3,4,1,3,4,X Where X=1,2,3,4 And τ is a topology of X. The group…

Q: What are the intervals where the function has a positive first derivative? (d,e) (b,c) (c,d) (e,f)…

A: Recall the fact that the first derivative is positive if the function is increasing in that…

Q: What is an average rate of change of function f(x) over the interval [1, 6]?

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Using forward, backward and central finite divided difference to find the first derivative of y = at…

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: We will use the average rate of change formula. f(x+h)-f(x)h

Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

The
values
in
the
table given below
calculated by means
of
are
function f(x) = x²-0,2·x² +x.
X
0,7
0,8
0,9
1,0
1,1
f(x)
0,945
1,184
1,467
1,800
2,189
a) From the above data set, find the numerical derivative values of f"(0,75)and f"(1,1) with
finite difference method.
b) Calculate the absolute relative error of the results according to the actual values from the given
function.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Single Variable$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Consider the function on the interval (0, 2π). (a) Find the open intervals on which the function is increasing or decreasing. (b) Apply the First Derivative Test to identifyall relative extrema. (c) Use a graphing utility to confirm your results.
Finite Divided DifferenceFind the first order derivative using backward, forward and central. f(x) = e^x - cos(x)given, xi = 0; h = 1
Find all relative extrema of the function. Use the Second Derivative Test where applicable. f(x) = cos x − x, [0, 4 ]
Find all relative extrema of the function. Use the second Derivative Test where applicable. h(x)=x-2cosx, [0,4pie]
Leth(x) = arctan(x2+ 2x). Find all critical values (if any) ofhand use the second derivative test todetermine where all the local extrema of the function are. You should show all your work calculatingthe second derivative.
A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides. State the formula for the volume of a rectangular prism (aka box). Express the volume formula as a function of x. What is the domain of V? Find the derivative of V(x) with respect to x. Find the function values at the critical number/s and at the endpoints. What is the largest possible volume of the box? What is the length of the side of the cut-out square that will make the box which has the largest possible volume?
Find all relative extrema and state the intervals where the function is increasing and decreasing. Show your work using the first derivative test. y= 2+3x-x^3
The function f(x) is continuous and differentiable on the interval [−2,6]. It is known that f(−2)=4 and the derivative on the interval satisfies the condition f′(x)≤3 for all x∈(−2,6). Determine an upper bound of the function at the right endpoint x=6.
Consider the function on the interval (0, 2π). f(x)=x/2+cosx a. Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)Increasing: (?, ?) decreasing: (?, ?) b. Apply the First Derivative Test to identify the relative extrema.relative maximum (x, y) = relative minimum (x, y) =
Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = xy + 3 x + 9 y critical point (x, y) = classification Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum valuerelative maximum value
Mean Value Theorem: If f is a continuous function on the closed interval [a,b] & differable on the open interval (a,b), then there exists such numbers, c, on that f’(c)=[f(b)-f(a)]/b-a. Sketch the graph of a function that satisfies both the hypothesis and conclusion of the mean value theorem. Mark on the graph the value(s) of c and the corresponding tangent line to the curve guaranteed by the MVT
What are the number lines for f(x), f'(x) and f''(x) ?? showing the convacity for this derivative function below thank you!