Answered: 7 1 lim represents the derivative of…

Math

Calculus

7 1 lim represents the derivative of some function f(x) at some number a. Find f(æ) and a. f(z) = a =

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

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 4.1E: aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line...

See similar textbooks

Related questions

Q: 5. Calculate the derivative of f(x) = Use this result to determine whether the sequ x2 + 1 an = n2.…

Q: Find the values of x at which the function has a possible relative maximum or minimum point. (Recall…

A: Given the function fx=1-xe2x The derivative of the function will be f'x=2e2x-2xe2x+e2x…

Q: Example C.W: by using the definition of the derivative, find dy/dx of the function 1- f(2) f(x) =…

Q: 1. Use limits to find the derivative of the following function at the point a = -1. 1 2x + 1 f(x)= =…

A: We have to find derivative

Q: 11 at x = 10 Find the derivative of f(x) = f' 10 |(Type an integer or a simplified fraction.) %3D

Q: (24) Let elt-x)A - B(x) 9(A) = (25) et Differentiating o(A) and setting the derivative equal to…

Q: To Sketch the Graphs of functions using Derivatives. Problem. Consider the function f(x) = 8x - x…

A: Follow the procedure given below.

Q: 65. If f and g are the functions whose graphs are shown, let Mx g(x)), v(x) = g(f(x)), and w (x) =…

Q: 4. The graph of f' (x), the derivative of f of x, is continuous for all x and consists of five line…

Q: 100 The derivative of the function 1 is equal to ecos z

Q: 1. a) From our class discussions, recall that the derivative of a function f at a is, by definition,…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: 11. Given the function below, what is its derivative? * f(x) = 2x - √x f'(x) = 2x C f'(x) = 2 - a 1…

Q: 13. Find the derivative of y = in terms of f, g, h, f', g' and h', where f, g, and h are functions…

Q: 4 4) (i) Find the equation of the tangent line at the point (2, 4) for the curve, f(x) = x². (ii)…

Q: Please answer the question and show the solution (do note that there are two parts to the question).

Q: The limit cos(x) – 1 lim с — 4т represents the derivative of some function f (x) at some number a.…

A: This question is about finding derivative about a point .

Q: 5. Consider the function h(x) whose derivative h' (x) = 3x2Vx3 + 8. (a) Find functions f and g such…

Q: 1 Suppose that f is a function given as f(x) We will compute the derivative of f at x = 3 as - 2x –…

Q: (x) = tan(V2x) 5. Find the value of c that satisfy the equation f'(c) = )-T(@) value theorem for the…

Q: 12. The Definition of the Derivative Find the formula for the instantaneous rate of change of f(x) =…

A: Given:

Q: 6/5 (3 - x). x5/6 The derivative of the function y = In is y' = %3D

A: we have to find derivative

Q: 3. 3. A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

Q: The limit x°-1 lim x→1 r - 1 represents the derivative of some function f(x) at some number a. Find…

A: We need to find f(x) and value of a.

Q: 3 7 h(x) 7 22 h’(x) 5 10 Selected values of the increasing function h and its derivative h’ are…

A: We will use the table to solve the question.

Q: 7. The table gives selected values for the derivative of a function f on the interval -2<x<2. If…

A: The answer is given below

Q: 2. Which statement is not true? a. If a function f (x) has a derivative at x, then it is said to be…

Q: 1. Consider the function f(x) given by its graph at which the points C, E and H are the inflection…

A: Let's find.

Q: 2 6. Consider f(x) x + 1 a. Find f'(x) using the formal definition of the derivative. b. Find the…

A: Solve the function

Q: 31 2- -5 -4/-3 -2 The above is the graph of the derivative f '(x). How many critical points does the…

Q: Please show step-by-step solutions.

Q: The limit (8+ h)² – 64 lim h→0 h represents the derivative of some function f(x) at some number a.…

A: We will find the f(x) and a by using limit definition as shown below

Q: 16. The first derivative of the function f is given by f'(x) = 3x* – 12x'. What are the…

A: Given: first derivative of a function as f'(x)=3x4-12x3To identify the points of inflection of…

Q: 3. If f and g are the functions whose graphs are shown below, let u(z) = f(g(x)), v(x) g(f(r)) and…

A: Given:- u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if…

Q: 2 a) Let f(x) =: Use the definition of the derivative to find f'(0). x+1 b) Let f(x) = Use the…

A: a) Given. The function f(x)=2x+1 The definition of the derivative: The derivative of the function…

Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

Q: 2. Let f(x) = cos(x). We will take derivatives of this function over and over. (a) Evaluate the…

A: Using standard formula of derivatives.

Q: 1 Let f(x) 4+ x -1 (a) Using the definition of derivative, show that f'(x) (No points if the…

A: the definition of the derivative is given by . the given function is substitute x+h for x

Q: 11. (a) Find F'(x) using the limit definition of the derivative if F(x) = F'(x) will result in zero…

Q: 7-1 lim represents the derivative of some function f(x) at some number a. Find f(x) and a. f(x) =

A: Here limx→07x-1x represents derivative of a function f(X) so first we need to evaluate the limit.…

Q: (b) If r is an R– R² function and f an R² – R function. State the General Chain rule for determining…

Q: ose k is the derivative of K, a function with the same domain as k. inction K has one critical point…

A: According to answer policy we can answer one question at a time, therefore I will be answering first…

Q: 13. Suppose f is a function whose first derivative is f'(x) = 1(x+1)(z-1)2(z-2). Sketch a sign chart…

A: Local maxima and minima

Q: 1) 2 a) Let f(x)=√x +4. Use the definition of the derivative to find f'(x). Find f'(5) by two…

Q: 1 Let f(x) X - 1 (a) Find the derivative f 'of f. 1 f '(x) = (x – 1) X* (b) Find an equation of the…

Q: 24 The following limit gives the derivative of a function f(a) at a point zo: √8th-2 lim h 0 h

Q: 11.6.19 Assigned Media Use the quotient rule to find the derivative of the given function. x² - 8x +…

A: The objective is to use quotient rule to find the derivative of the given function.

Q: 4x Consider the function f(x) : 3 – x a. Use the \underline{limit definition of derivative} to find…

A: We can solve all these points in the following way:-

Q: 1) Suppose the second derivative of a contiovous function given by f"(x)=Cx-2 )3 (x-2)2 (sx-) A…

Q: 1. The figure below shows the graph of f', the derivative of the function f, on the closed interval…

A: Given

Question

7 - 1
lim
represents the derivative of some function f(x) at some number a. Find f(x) and a.
f(x)%3D
%3D
a =

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

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
aThe average rate of change of a function f between x=a and x=b is the slope of the ___________ line between (a,f(a)) and (b,f(b)).