Tuesday

September 2, 2014

September 2, 2014

Posted by **Britney** on Sunday, November 11, 2012 at 9:46pm.

Where are the relative extrema, if they exist?

- math -
**Reiny**, Sunday, November 11, 2012 at 11:23pmfrom your previous post

x = 0 or x = 3

so

f(0) = 10

f(3) = 81 - 108 + 10 = -17

f '' (x) = 12x^2 - 24x

f '(0) = f ''(0) = 0

so (0,10) is a point of inflection

f ''(3) = 108 - 72 > 0

so at (3,-17) the curve is concave upwards, so

(3,-17) is a minimum point

look at the sketch

http://www.wolframalpha.com/input/?i=plot+x%5E4-4x%5E3%2B10

**Answer this Question**

**Related Questions**

math - Find the relative extrema, if any, of the function. Use the second ...

Calculus - Find the relative extrema, if any, of the function. Use the second ...

math - let f(x)=x^3+3x^2-2x+4 What are the critical values? Where are the ...

math - let f(x)=x^3+3x^2-2x+4 What are the critical values? Where are the ...

math - Let f(x)= x^4-4x^3+10 Where are the relative extrema, if they exist? Show...

math - Let f(x)= x^4-4x^3+10 Where are the relative extrema, if they exist? Show...

Calculus - Find the intercept, relative extrema, point of inflection, and ...

Calculus - Find the intercept, relative extrema, point of inflection, and ...

Calculus - Find the intercept, relative extrema, point of inflection, and ...

Calculus - Find the intercept, relative extrema, point of inflection, and ...