Find the absolute extrema of the function f(x)=3x^4-4x^3on [-1,2]

Question

this problem is complicated any help?

Answer 1

To decide on the extrema, check for maximums & minimums and compare them to the values at the endpoints.

 

First, take the derivative to find the critical points (places of possible maximums and minimums):

 

f'(x) = 12x³ - 12x² = 12x²(x - 1)

 

f'(x) = 0 when x = 0 or x = 1.

 

 

Check the critical points against the end points:

 

f(-1) = 7   (end point)

 

f(0) = 0    (critical point)

 

f(1) = -1   (critical point)

 

f(2) = 16   (end point)

 

The absolute minimum is at x = 1 and the absolute maximum is at x = 2.