Find the absolute minimum and absolute maximum value

Question

Find the absolute maximum and minimum values of the following function over the indicated​ interval, and indicate the​ x-values at which they occur.

​f(x)=13x^3+52x^2−24x+3​;

​[−10​,4​]

The absolute maximum value is

nothing

at

x=nothing.

The absolute minimum value is nothing at x = nothing

Answer 1

13x^3 +52x^2 - 24x + 3

f'(x) = 39x^2 +104x -24 = 0

x =about 0.214 or -2.880

f(0.214) is a relative local minimum = about 0.118

f(-2.880) is a relative local maximum = 192.8889

f(-10) = absolute minimum = -7,557

f(4) = absolute maximum = 1,571

if you go beyond the [-10, 4] interval

f(x) approaches + infinity as x approaches + infinity

and f(x) approaches - infinity as x approaches - infinity