Let F(x) = f(x¹) and G(x) = (f(x))¹.You also know that a³ = 10, ƒ(a) = 2, ƒ'(a) = 6, ƒ'(aª) = 4Then F'(a)=and G'(a)= Find the following using the table below.X1 2 3f(x) 4 1 2 3f'(x) 4g(x)g'(x) 4 1 2NW1 2h' (3) if h(x) =433W|N34 1 3 2W|N3h' (3) if h(x) = f(x) · g(x)f(x)g(x)h'(3) if h(x) = f(g(x))

Answered: Image /qna-images/answer/7c305a54-c3c8-41d0-871a-29411279d530.jpg

Answered: Let F(x) = f(x¹) and G(x) = (f(x))¹. 3…

Let F(x) = f(x¹) and G(x) = (f(x))¹. 3 You also know that a³ = 10, ƒ(a) = 2, ƒ'(a) = 6, ƒ'(aª) = 4 and G'(a) Then F'(a) =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.1: Techniques For Finding Derivatives

Problem 36E: Find all points on the graph of fx=x3+9x2+19x-10 where the slope of the tangent line is -5.

See similar textbooks

Related questions

Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

Q: 13. The graph of the first derivative f'(x) of a function is shown. Identify the graph of f. N

A: Given query is to find the the graph of the function from the derivative graph.

Q: A tube is being stretched while maintaining its cylindrical shape. The height is increasing at the…

A: NOTE: Refresh your page if you can't see any equations. . (height is increasing at a rate of 2…

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: Here we can create the required polynomial function in the below steps.

Q: 1. Find the center on the line y = x and passing through the origin. differential equation…

A: Need to find out the differential equation that represents the circles with center on the line y=x…

Q: implicit differentiation to find ∂z/∂x and ∂z/∂y if 3x^2+4y^2+2z^2=5 ∂z/∂x=________________…

A: Given query is to find indicated partial derivatives.

Q: These are the following jokes about books:. “Outside of a dog, a book is man’s best friend. Inside…

A: Given data Six jokes about books.

Q: A car sharing service offers a membership plan with a $30 per month fee that includes 10 hours and…

Q: A corporation has seven members on its board of directors. In how many different ways can it elect a…

A: There are 4 different positions: president, vice-president, secretary, and treasurer. Therefore, we…

Q: Evaluate the following integral, showing all calculus and algebra work. 2x² √2x²+x=1d + x - 1 -dx

Q: a. Distribute b. Solve { ª²³ (a²³ + 2a ²).

Q: Telephone numbers in the United States begin with three-digit area codes followed by seven-digit…

A: Given: Number of digits in area code = 3 Number of digits in local telephone number = 7 Total…

Q: A triangle has vertices (0, 0, 0), (1, 1, 1), and (0, −8, 9). Find its area.

Q: Draw the following intervals on the number line. 1. [ -1, 4] 2. (4, 3p) 3. [ -2, 12) 4. [1, 32] 5.…

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

Q: Explain how the range of the function f1x2 = x2compares to the range of g1x2 = f1x2 + k.

A: Given: f(x)=x2 To explain: How the range of f(x) compares to the range of g(x)=f(x)+k.

Q: Evaluate f(x) ƒ(1) = f(x + 7) = f(x) + f(7) f(x + h) = = = x + 2 at the indicated values.

Q: Solve the following equations. Leave answer in exact form. 1. e³x = 5 2.5e-7 = 8

A: Given, e3x=5Taking ln on both sideln(e3x)=ln(5)We know that ln(ab)=bln(a)3xln(e)=ln(5)We know that…

Q: Find the directional derivative of f(x, y) = direction of Q(2, −2). NOTE: Enter the exact answer.…

Q: A consumer purchased a computer after a 20% price reduction. If x represents the computer's…

A: A consumer purchased a computer after a 20% price reduction. If x represents the computer's…

Q: Use the washer method to find the volume of the solid obtained by rotating the region bounded by y =…

Q: Evaluate the derivative of the following function. 1) 6x H(x)= (5x +

Q: lim 1 - cos(sin(³-1)) 73 - 1

A: As per the instruction, we will be answering the first question. The graph of y=1-cossinx3-1x3-1.

Q: Find the derivative of the function. f(x) = arcsin (et) f'(x) = Find the domains of the function and…

A: To find out the derivative of the function.

Q: Homework 3.3 For #1-8, differentiate 1. f(x) = x² cos x

Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y - 2z subject…

Q: Consider the following limit statement: lim (9x-3) 15 x → 2 Find the corresponding value of 6 when &…

A: givenlimx→39x-3=15

Q: Find the limit, or show that it does not exist. 2x - y lim (x,y) (0,0) y + x²

Q: FIND F'(x) for F(x) = -7 w/out USING the √5x³-20x quotient TULE

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

Q: Use algebra to rewrite the expression BEFORE you differentiate. 8x¹7 - 2x¹4 14 x11 A) 32x³ - 2x D)…

Q: State whether the equation is ordinary or partial, linear or non-linear, and give its order and…

A: See this solution in below.

Q: Set up the integral to be used to find the volume V, using both methods from Chapter 7, of the solid…

Q: A car has 12,500 miles on its odometer. Say the car is driven anaverage of 40 miles per day. Choose…

A: Given data:- A car has 12500 miles on its odometer Car is driven an average of 40 miles per day N is…

Q: If ƒ(1) = 5, must lim x approaches 1 ƒ(x) exist? If it does, then must lim x approaches 1 ƒ(x) = 5?…

A: Given :-f(1)=5Now, we have to find that limx→1f(x) exists or not.And if limx→1f(x) exists then…

Q: Evaluate O 3π S sinx dx using the fundamental theorem of calculu 3π sinx dx = 0 3πt A-4 sinx dx =…

Q: determine whether the given function is linear or nonlinear. If it is linear, determine the equation…

A: Note:- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find all the first and second order partial derivatives of f(x, y) = −4 sin(2x + y) + 10 cos(x - y).…

A: Given:- fx,y=-4sin2x+y+10cosx-y

Q: Learning Goal: To understand the continuity equation. Streamlines represent the path of the flow of…

A: part A Q=A1v1 Part B v2=A1v1/A2 Part c velocity

Q: Elimination of Arbitrary Contants 1. y = peax cosbx + yeax sin bx 2. y = c₁x + c₂ex ; a and b are…

A: we need to eliminate the arbitrary constants C1 and C2

Q: Suppose that f(x, y, z) = x²yz — xyz³ is a function of three variables. 1. Find the gradient of f(x,…

Q: Devise an exponential decay function that fits the given data, then answer the accompanying…

A: Here, the equation used is: P=P0ekt...(1) where P is the pressure of the atmosphere at t=0 and k is…

Q: True or False The slope of a nonvertical line is the averagerate of change of the linear function.

A: The average rate of change of the linear function is the slope of a nonvertical line.

Q: In this exercise you will conclude that a limit does not exist by computing the limiting using two…

Q: Use limits involving to to describe the asymptotic behavior of the function from its graph. (If an…

A: From graph f(x) goes towards 1 at left end of graph

Q: Evaluate the following integral. 4 ex S- 2x 9- e -dx

A: See this solution in below.

Q: Use the chain rule to find the derivative of f(x) = 4√9x7+7x10 Type your answer without fractional…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: If the slope m of the graph of a linear function is ,the function is increasing over its domain.

A: If the slope m of the graph of a linear function is _______, the function is increasing over its…

Q: Shown below is the graph of the flow rate f(t) of a pipe, in gallons per minute. Here, t= the number…

Q: Find the area bounded by the curves x y = 8 (in green), y blue) and the line 3y sliced pizza? 2 =…

A: Let's find area of the sliced pizza.

Q: A restaurant dinner menu includes the following statement. "All dinners are served with a choice of:…

Q: In 2004, an art collector paid $172,536,000 for a particular painting The same painting sold for…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Question

Let F(x) = f(x¹) and G(x) = (f(x))¹.
You also know that a³ = 10, ƒ(a) = 2, ƒ'(a) = 6, ƒ'(aª) = 4
Then F'(a)
=
and G'(a)
=

Find the following using the table below.
X
1 2 3
f(x) 4 1 2 3
f'(x) 4
g(x)
g'(x) 4 1 2
NW
1 2
h' (3) if h(x) =
433
W|N
3
4 1 3 2
W|N
3
h' (3) if h(x) = f(x) · g(x)
f(x)
g(x)
h'(3) if h(x) = f(g(x))

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