Is f(x)=4x^5-12x^4+5x^2+2x+2f(x)=4x5−12x4+5x2+2x+2 concave or convex at x=-5x=−5?

1 Answer
SCooke
May 4, 2018

Concave

Explanation:

We use the second derivative to determine the curvature of a function. It is concave if the second derivative is less than zero and convex if the second derivative is greater than zero.
enter image source here

enter image source here
enter image source here

Weisstein, Eric W. "Second Derivative Test." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SecondDerivativeTest.html

f(x)=4x^5−12x^4+5x^2+2x+2f(x)=4x5−12x4+5x2+2x+2

f'(x)=20x^4−48x^3+10x+2

f''(x)=80x^3−144x^2+10

f''(-5) = 80(-5)^3−144(-5)^2+10

f''(-5) = -10000 − 3600 + 10 = -13590

Definitely negative, so it is concave.

Related questions
See all questions in Analyzing Concavity of a Function
Impact of this question
1651 views around the world
You can reuse this answer
Creative Commons License