Question
Asked Apr 1, 2019
15 views

Please help

2. Suppose that the graph of y - f(z) lies entirely above the r-axis and f'(r) <0 for all r
Let g(x) = (f(x))2 and h(z) = f( 2). For each one of the functions g and h, answer the following
questions
a) Determine the critical points of the function or explain why there are none.
b) Determine the intervals where the function is increasing and the interval(s) where the function is
decreasing
help_outline

Image Transcriptionclose

2. Suppose that the graph of y - f(z) lies entirely above the r-axis and f'(r) <0 for all r Let g(x) = (f(x))2 and h(z) = f( 2). For each one of the functions g and h, answer the following questions a) Determine the critical points of the function or explain why there are none. b) Determine the intervals where the function is increasing and the interval(s) where the function is decreasing

fullscreen
check_circle

Expert Answer

Step 1

(A)

Calculation of critical point of g(x):

we can find derivative 

We can see that f(x) is positive and f'(x) is negative 

and g'(x) is multiplication of both f(x) and f'(x)

So, g'(x) will become negative because positive*negative =negative

 

fullscreen
Step 2

Since, it is always negative 

So, it can not be equal to 0

So, no critical point exist

Answer: 

No critical point for g(x)

Step 3

Critical point for h(x):

we can find derivative of h(x)

and then we can set derivative to 0 

and then we can solve for x

we kno...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Related Calculus Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: differentiate f(t) = t^(1/3)/ (t-3) On the solution guide on the first step for the numerator, we ha...

A: Explanation:Consider the term t1/3.It is known that adding and subtracting a same number to any numb...

question_answer

Q: Hello,  I need help understanding how to form a general formula, using f(x)=5 tan x, for all the sol...

A: Consider the provided function.

question_answer

Q: :)

A: Given:The given curves are y = x2, x = 1, and y = 0.The volume of the solid revolved around the line...

question_answer

Q: 3ln xy′−9x2 y′=4x4  What is the order of the differential equation shown above?

A: The given differential equation is ,3ln xy′−9x2 y′=4x4  The order of the differential equation is th...

question_answer

Q: Consider the function g(x) = |(x^2 - 4)/(x+3)| do the following: a) Give the domain of the function ...

A: a) First obtain the singularity for the given function as follows.The denominator of the given fract...

question_answer

Q: Find the relative maxima, relative minima, and points of inflection and sketch the graph for the fun...

A: We have to find the relative maxima, relative minima, and points of inflection and sketch the graph ...

question_answer

Q: Determine if y=e−x+8x−9 is a solution to the initial value problem given by y′+1=8x−y and y(0)=−8.

A: The given differential equation is y′+1=8x−y.The solution of the deferential equation is given as, y...

question_answer

Q: For the function y=x-1/3x^3 (a) Find the coordinates of the relative maxima, relative minima or hori...

A: (a) The function is given as

question_answer

Q: Part d and e

A: (D) When the enclosed region revolve about x=2 line then the radius is on the line joining (2,0) and...