Question
Asked Apr 5, 2019
6 views
r2
r2-1
onsider the function q(r
minimum and maximum values or q
(b) Find the intervals of concavity and inflection points of g(x)
help_outline

Image Transcriptionclose

r2 r2-1 onsider the function q(r minimum and maximum values or q (b) Find the intervals of concavity and inflection points of g(x)

fullscreen
check_circle

Expert Answer

Step 1

(a). For any given function f(x), the local maximum or minimum exists at a point where x = a if f’(a) = 0

Applying derivative to the function with respect to x:

 

So for local maximum or minimum: 

Hence, the local maximum or minimum exists at x = 0

fullscreen
Step 2

A point is said to be local maximum when f’'(x) < 0 and is said to be local minimum when f’'(x) > 0

Applying derivative to the first derivative:

Checking the value of this function at x = 0,

 

Since g''(0) < 0, local maximum exists at x = 0

Hence, the local maximum is given by:

 

Therefore, the local maximum value is 0 and the local minimum does not exist.

fullscreen
Step 3

(b)

A function f(x) has inflection points at x = a if f’'(a) = 0

Hence, the inflection point for the function g(x) is given by:

 

Hence,...

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: Need a,b, and c please!

A: The given equation is s = –0.2t2 + 12t and the velocity is v =12 m/s. a. Obtain the velocity v of th...

question_answer

Q: Which of the following limits could be evaluated using L'Hopital's Rule? Indicate all the apply. Sel...

A: (A) This limit was not in form 0/0 or infinity/infinity. So we can\'t apply L\'Hospital\'s rule for ...

question_answer

Q: Please show as much steps as possible as I am doing my best to fully understand how to solve these t...

A: Given function is, 

question_answer

Q: Use Newton's method to approximate all intersection points of the following pair of curves. Round to...

A: Before we get into the solution of the question, let's understand a bit about Newton's method. If xn...

question_answer

Q: Logarithmic Differentiation - See attachment

A: Find the derivative of the given function.

question_answer

Q: find the domain and range of f(x)=X5+x (the last x is supposed to be squared) and domain and range o...

A: Given information:The given function is f(x)=X5+x^2  and g(y)=1/y-2.

question_answer

Q: Find the power series representation for g centered at 0 by differentiating or integrating the power...

A: Consider the geometric series,

question_answer

Q: Determine the location and value of extreme values of f on the given interval, if they exist.   Type...

A: Given information:The given function is  

question_answer

Q: 3 dx = 1 2x 8 In 국 5 -4 In 2 In을 -2 In -8 In LOn LOn

A: Obtain the value of the integral as follows.The given integral is,