Question

calculus help again!

Answer 1

Find the absolute max and min of \[f(x)= -12x+3x ^{2}+ 2x ^{3} in \left[ -1,2 \right]\]

Answer 2

HI!!

Answer 3

take the derivative, set it equal to zero to find the critical points, then check them and also the endpoints

Answer 4

derivative should be easy enough since it is a polynomial
the derivative will be a quadratic
maybe you can factor it

Answer 5

did you solve
\[6x^2+6x-12=0\]?

Answer 6

I was able to figure out that the critical number are -2, -1, 1,2. -2 doesn't fit into the oringianl interval given, so would i just ignore it or would (-2, 32) be my absolute max?

Answer 7

The roots are -2,1. And you need find something else, like
f(-2) =20
f(1)=-7
moreover, f(-1), f(-2) those are from interval.
f(2) = 4
f(-1) =13.05
Hence from the interval [-1,2] f(-1) is max, f(1) is min