`f(x) = 3x^4 - 4x^3 - 12x^2 + 1, [-2, 3]` Find the absolute maximum and minimum values of f on the given interval
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Given: `f(x)=3x^4-4x^3-12x^2+1,[-2,3].`
Find the critical numbers by setting the first derivative equal to zero and solving for the x value(s).
`f'(x)=12x^3-12x^2-24x=0`
`12x(x^2-x-2)=0`
`12x(x-2)(x+1)=0`
`x=0,x=2,x=-1`
The critical numbers are x=0,x=2, and x=-1. Plug in the critical numbers and the endpoints of the interval [-2,3] into the original f(x) function.
f(-2)=33
f(-1)=-4
f(0)=1
f(2)=-31
f(3)=28
Examine the f(x) values to determine the absolute maximum and...
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