# Maximum and minimum values

Not what you're looking for?

Given: y = f(x) = 3x4 + 4x3

Find:

A. All critical points

B. Max - Min Values

C. Inflection points

D. Where is f(x) concave up

E. Where is f(x) concave down

F. X and Y intercepts

G. Where f(x) is increasing

H. Where f(x) is decreasing

I. Sketch the curve label

##### Purchase this Solution

##### Solution Summary

This shows how to find critical points and concavity.

##### Solution Preview

f(x) = 3x^4 + 4x^3

=> f'(x) = 12x^3 + 12x^2 = 12x^2(x+1)

=> f''(x) = 36x^2 + 24x

=> f'''(x) = 72x + 24

=> f''''(x) = 72

A.)

For critical points:

f'(x) = 0 => 12x^2(x+1) = 0

=> x = 0, -1 --Answer

B.)

=>f''(0) = 0 : Neither max nor min

=> f'''(0) =

f''(-1) = 36 - 24 = 12: minima

f(infinity) = infinity

f(-infinity) ...

###### Education

- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

###### Recent Feedback

- " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
- "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
- "Answer was correct"
- "Great thanks"
- "Perfect solution..thank you"

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Probability Quiz

Some questions on probability

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.