Absolute maximum and absolute maximum

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

Take the first derivative of the function (a quadratic) and find the x values for which it equals 0 using quadratic formula.

You can plug in the two values and the endpoints in order to find out if you a have an absolute min or max. The second derivative at the critical points can tell you if you have a relative min or max, but you always have to check the endpoints of the interval if those points are in the domain to ascertain if they are global min or max.

Since you are testing the max and min by plugging in to f(x) you will automatically have the function values at the absolute min and max for the interval.