Find the absolute maximum and absolute minimum values of f (x) = ^3√t(8 − t) on [0, 8].

Answer 1

Sophia,

I assume f(t)=cube root of (t*(8-t)

the derivative numerator wind up being (8-2t)

so at t=4 the derivative is zero, that is there is critical point and since before

t=4 the numerator is positive and after negative

this is a maximum. At t=4 the denominator is positive.

At t=4 f(t)=the cube root of 16.

the minimums are at the endpoints, t=0 and t=8

where f(t)=0