Calculate the average rate of change of the function f(x)= 15x-3x^2 near a=5 over the intervals [a,a+h]

Q: find the average rate of change of the function overthe given interval or intervals. ƒ(x) = x3 + 1…

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Q: Find the average rate of change of the function on the interval specified. h(x) = 3 − 6x2  on  [−2,…

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

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Q: On which derivative rule is integration by parts based?

A: Integration by parts is based on product rule of derivative. Mathematically, Product rule of…

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: Find the average rate of change for function over the given interval.

A: Given  y=3x-2.

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: Find the points on the graph of f where the tangent line is horizontal. tangent line is 3x^2-16…

A: The tangent line is horizontal where y'=0

Q: 2. Determine the second derivative of f(x)= x'e* at x = -2 with a step-size of h=0.50 using Central…

A: Given function is f(x) = x2e2x and h = 0.50

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: Explain the concept of differentiation and integration.

A: Differentiation and integration are the process of calculus in mathematics. In differentiation, we…

Q: Estimate the slope of the tangent line at the point x = 3, for f(x) = In(x). (Use decimal notation.…

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Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

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Q: Find the anti-derivative: x2/3 dx. Upload Choose a File

A: Using simple integration method to solve the question.    Attached below is the detailed solution.

Q: tion of the tangent line to f(x) = 4 %3D

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Q: The total derivative of f(x,y) = ylnx  is

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Q: An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A: We will estimate the volume of cylindrical metal as following. Inside radius = 2 cm Inside height =…

Q: Use differentials to approximate the increase in the area of a soap bubble when its volume increases…

A: Let the radius of the soap bubble be a cm, then the volume of the soap bubble is: V=43πr3        And…

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: Are critical numbers from the first derivative used in the test for concavity?

A: We have to tell that  critical numbers from the first derivative used in the test for concavity or…

Q: What formula will describe the average rate of change of f(x) = 3* over the interval [0, 3]? Don't…

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Q: find the average rate of change of the function overthe given interval or intervals. g(t) = 2 + cos…

A: Given, g(t)=2+cost, -π,π The average rate of change of function f(x) over an interval [a,b] is,…

Q: Estimate the derivative of f(x) = sinx at x = π/6

A: Since,it is known that the derivative of the function with any variable measures the rate of change…

Q: Find the average rate of change of the function from x, to x,. Function x-Values f(x) = x² – 3x + 8…

A: The given function and x -values are: fx=x2-3x+8, x1=1, x2=5 Now, calculate the average rate of…

Q: Find the derivative of f(x)=ex/(sqrt x) at x=1. Round your answer to 4 decimal places.

A: Find the derivative of f(x) = ex/(sqrtx) at x=1 round your answer to 4 decimal places. We know that…

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: Find the average rate of change of f(x) = 8x2 - x:(a) From 1 to 2       (b) From 0 to 1     (c) From…

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Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: Determine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at…

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Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

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Q: Estimate approximate derivative of f(x) = x2 at x = 1, for h = 0.2, 0.2, 0.05, 0.01 using first…

A: Given function is fx=x2. We have to estimate approximate derivative of the given function at x=1 for…

Q: Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on  [−2,…

A: To Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on…

Q: Find the average rate of change of LaTeX: f\left(x\right)\:=3x^2+1 f ( x ) = 3 x 2 + 1 between…

A: Formula for average rate of change is f(b)-f(a)b-a.

Q: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average value over [0, 1]? Over [1, 2]?

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Q: Can the  derivative of f(x) be zero in the interval [-1,0]

A: Given, fx = x4+8x+3  f'x = 4x3+3   We have to find the derivative of fx be zero in the interval -1,0…

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: What is the relationship between the secant line, slope of the tangent line, derivative of a…

A: Solved below

Q: 2. Determine the second derivative of f (x)=xe* at x = -2 with a step-size of h=0.50 using Central…

A: Given f(x) = x2e2x

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: Calculate the derivative of the function y=arccos x arctan x at x=0.

A: Differentiating with respect to x, we get

Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: Find the average rate of change of the function on the interval specified Y=1/x on [1,3]

A: We know that ,The average rate of change of function over an interval a,bis given by f(b)-f(a)b-a

Q: Find the maximum rate of change of f(r,y) = sin(x + y) at the point (1,-1) and the direction at…

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Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

Q: 1 f(x) = (x² + 3x)² at [2,3]

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Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

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Exponential Growth Model

The relation that represents an exponential function is: