Expert: Paul Klarreich - 3/5/2010

Question
Use the Second Derivative Test to find all relative extrema of the function.

f(x)=2x3+3x2-12x+16
two x to the third power plus three x squared minus tweleve x plus sixteen.

Answer
Questioner: Gabriel
Country: United States
Category: Calculus
Private: No
Subject: Survey of Calculus
Question: Use the Second Derivative Test to find all relative extrema of the function.

f(x)=2x3+3x2-12x+16
two x to the third power plus three x squared minus tweleve x plus sixteen.
.........................................

Find the critical points:

Set f'(x) = 6x^2 + 6x - 12 = 0  and solve:

You will get:

x = 1,  x = -2

Compute y = f(1),  y = f(-2), so you have the actual points.

Find f''(x) = 12x + 6

Compute  f''(1).  
  If it is negative, say 'MAXIMUM'.
  If it is positive, say 'MINIMUM'.

Compute f''(-2)
  If it is negative, say 'MAXIMUM'.
  If it is positive, say 'MINIMUM'.

That should do it.