The elevation of a path is given by f(x) = x^3 - 5x^2 + 30, measured in feet, where x measures horizontal distances in miles. Draw a graph of the elevation function and find its average value for 0 <= x <= 4

Q: Can a function have an inflection point at a critical point? Explain

A: Show that: Can a function have an inflection point at a critical point?

Q: Apply the First Derivative Test to identify all relative extrema. f(x) = -7x³ + 21x +3

A: fx=-7x3+21x+3 Differentiating with respect to x, we get f'x=-73x2+211+0⇒f'x=-21x2+21 Now to find…

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x³ + 15x² + 24x – 3

A: We Know that The second derivative may be used to determine local extrema of a function under…

Q: Find the derivativeof ƒ(x) = x5. Then find the samederivative using the Quotient Rulewith ƒ(x) =…

A: Given: We have to find the derivative of f(x)

Q: Find derivative using product or quotient rule

A: f'(x)=((x2)'(x+3)(4x-1)-x2((x+3)(4x-1))')/((x+3)(4x-1))2       (Using quotient rule)…

Q: How is derivatives utilized in solving for the dimensions and total area of a box?

A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

Q: Find the average rate of change of the function over the specified interval. f(x) = 2x2 - 3x - 4,…

A: The given function is f(x)=2x2-3x-4 ; [-2,1]

Q: Use the first derivative test to locate all local extrema for 3 f (x) = -x'+ = -x' +- x +18x.

A: Explanation of the answer is as follows

Q: Find the average rate of change of f(x) = 3x2 - 5 from x1 = 6 to x2 = 10.

A:

Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

A:

Q: Use derivative rules to find f'(x). 4. f(x) = (2x² – 3)(3x – 1) -

A: f(x) = (2x2-3) (3x-1)derivative rulef(x).9(x)' = f'(x)9(x)+f(x)g'(x)or (uv)' = u'v+uv'

Q: Find the average rate of change of g(x) = 4x + 2 between the points (-3,-10) and (3,14)

A:

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=7−67xf(x)=7-67x, and the line…

A:

Q: use th eproduct rule or the quotient rule to find the derivative of f(x)=(x^2+x-8)/x^2-8

A:

Q: Use the second derivative test to find the extre #1) f(x) = x³ + 2x² - 4x-8 %3D

A:

Q: Find the absolute extrema of the function on the closed interval.

A: Given,  The function is  y=3-t-3 Interval is [-1,5] The given function is a modulus function which…

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=3−16xf(x)=3-16x, and the line…

A: GIVEN DATA: Triangle is bounded by the equation of line fx=3-16x                         line…

Q: Use the second derivative test to find the local extrema for the function. y = 3x5- 25x3 + 60x + 20

A: We can use the application  derivative in order solve the given problem.

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Find the critical points and apply the Second Derivative Test (or state that it fails): f (x) = x5 −…

A: f(x)=x5-x3

Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: Use Intermediate Value Theorem to show that the equation

A:

Q: Apply the second derivative test to find all relative extrema. (b) f(x) = -x + 4x³ +8x²

A:

Q: Use Second Derivative Test to find the location of all local extrema for f(x)=2x³+21x²+36x-1

A: Local extrema.

Q: Find the x-value for all relative extrema of f(x) using the first derivative test. Specify whether…

A:

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

A:

Q: Find the extreme values of the function f(x)=x√√1- x .- x on the interva

A:

Q: Use the second derivative test to find the extreme values of the function f(x) = 13 -3z2-24x

A: Given: f(x)=x3-3x2-24x To find the extreme value of the function.

Q: Compute the derivative f(x)= cubed root of x + 3/x5

A:

Q: Find the average rate of change of f(x)=6xsquared -8 on the interval [1,a]

A:

Q: Find the average rate of change of f(x) = 3x2 - x from x1 = -1 to x2 = 2.

A: The given function is fx=3x2-x.

Q: Find continuous functions

A: Given,        fn:0, 1→[0, ∞)

Q: How do you use the second derivative test to analyze concavity of a function?

A: We know that, If the second derivative of the function f(x) is defined on an interval (a,b) and…

Q: What is the derivative of a function f(x) = 4x³ – 3x2 at a number a? %3D

A:

Q: average rate of change

A:

Q: differentiate the function (use long method)   y=secx

A:

Q: find the average rate of change of f (x)= 5x3 - 6x2 - 10x+9 on the interval [-4,6]

A: We will use the average rate of change formula  f(b)-f(a)b-a. Here a=-4 and b=6

Q: Differentiate the function. y= (5x- 5) (5 -x*)5 - 15625(x – 1)ª (5 – x*)*(5+4x³ – 5x*) dx

A:

Q: Use Second Derivative Test to find the location of all local extrema for f(x) = 2x3+21x²+ 36x-1

A:

Q: Compute the average rate of change of f(x) = x2-1/x on the interval of [2,4]. Please show me each…

A:

Q: Use the second derivative test to find all relative extrema  f(x)= x+4/x

A: The given function is as - f(x) = x+4xProcedure to find local extremas - 1. Find f'(x)2. Put f'(x) =…

Q: Use derivative rules to find f'(x). 4. f(x) = (2x² - 3)(3x – 1) %3D

A:

Q: Find the derivativeof ƒ(x) = x5. Then find the samederivative using the Product Rule withƒ(x) = x2…

A: We have to find the derivative of the function: fx=x5 We have to find same derivative with product…

Q: find the average rate of change of f(x) = -x3+3x2 from x=-1 to x=4

A:

Q: Find the x value for all relative extremes of f(x) using the first derivative test. And specify…

A: Given,            f(x) =x2 - 15x - 15x + 1

Q: Find the average rate of change of g(x) = 5x2 + (5)/(x4) on the interval [-4,3].

A: Given, g(x)=5x2+5x4 And given interval is -4, 3

Q: differentiate the function: f(x) = 6x ln(5x) -6x f'(x)=

A: Use sum rule for differentiation.

Q: find the average rate of change for f(x)= 3x2-x+5 from x=2 to x=2+h in simplified form

A: Given function:

Q: Find the higher order derivative. f"(x) = 4x2 + 9x – 16 - f(5)(x) = %3D

A:

Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…

Exponential Growth Model

The relation that represents an exponential function is: