find the average rate of change f(x)=8x^2-2 on the interval [5,a]

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

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Q: What is the First Derivative Test for Local Extreme Values?

A: What is the First Derivative Test for Local Extreme Values?

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 average rate of change of f(x) = x² - x + 1 from x, = 1 to x, = 3. %3!

A: We have to find the average rate of change of function fx=x2-x+1 from x1=1 to x2=3. We know average…

Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

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Q: What is the average rate of change of the function f ( x ) = 3 x over the interval [ 2 , 5 ]

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Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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Q: Apply the second derivative test to find all relative extrema. - 5)² (a) f(x)=(x

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Q: Explain the derivatives and integration.

A: Solution: Derivatives: Definition of derivatives is , the rate of change of a quantity with respect…

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

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: Use differentials to estimate the value. estimate =  exact value =

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Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

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

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Q: Find the average rate of change of the function over the interval [-2, 1] f(x) = 2.x³ – 5.x +3

A: To determine the average rate of change of the below function over the interval [-2,1]. fx=2x3−5x+3

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: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

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

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Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

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 dy ldx by Tmplicit differentiation. tanLx-y)=

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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: 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: Find the average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to…

A: Since it is known that the average rate of change can be calculated using the formula…

Q: What is the average rate of change of y with respect to over the interval [-1, 2] for the function y…

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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: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

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

A:

Q: Explain how the Second Derivative Test is used.

A: The second derivative may be used to determine local extrema of a function under certain conditions.…

Q: 7) Find the average rate of change of the function A(x) = sin ( 2x - -) from x = to x =

A: A(x) = sin(2x - π/6) A(x2) = A(5π/6)          = sin(2*5π/6  - π/6)          = sin (9π/6)          =…

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: 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: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

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

A: Solved below

Q: Find the points on the graph of f where the tangent line is horizontal. f(x) = x3 - 18x2 (x, y) = (…

A: As we know that the slope of the tangent on a graph represents by f '(x) and it is parallel to the…

Q: What is the average rate of change of f(X)= X2-2 on the interval [-1,3]?

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

A: Differentiating with respect to x, we get

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: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: Find the derivative of s(*) - L Int dt 1+t

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Q: What is the average rate of change of f between x=3 and x=10

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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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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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Exponential Growth Model

The relation that represents an exponential function is: