SOLUTION: Let g(x) = x^4 - 6x^2 - x - 3 Find the maximum value and the minimum value of the 2nd derivative g" on the interval [-1,2] Please show the steps to solve. Thank you

Algebra ->  Test -> SOLUTION: Let g(x) = x^4 - 6x^2 - x - 3 Find the maximum value and the minimum value of the 2nd derivative g" on the interval [-1,2] Please show the steps to solve. Thank you      Log On


   

Question 983091: Let g(x) = x^4 - 6x^2 - x - 3
Find the maximum value and the minimum value of the 2nd derivative g" on the interval [-1,2]
Please show the steps to solve.
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the second derivative.
First derivative,
dg%2Fdx=4x%5E3-12x-1
Second derivative,
%28d2g%29%2F%28dx2%29=12x%5E2-12=12%28%28x-0%29%5E2-1%29
So the second derivative, in vertex form, has a vertex of (0,-1).
Since the multiplier is positive 12%3E0, it opens upwards so the value at the vertex is the minimum.
(0,-12)
.
.
.
The maximum occurs at the endpoints specifically at x=2 since it is further away from the axis of symmetry x=0.
(0,36)