# Max values of a function in a given interval

Find the maximum of f(x) = x^4 = 6x^3h + 11x^2h^2 - 6xh^3 at [0,3h]

© BrainMass Inc. brainmass.com October 10, 2019, 6:15 am ad1c9bdddfhttps://brainmass.com/math/optimization/max-values-function-interval-536155

#### Solution Preview

f(x) = x^4 - 6 x^3 h + 11x^2 h^2 - 6 x h^3

can be factorized as:

f(x) = (x - 0) * (x - h) * (x - 2h) * (x - 3h)

Hence, f(x) intersects with X axis at points x =0; x = h; x = 2h & x = 3h

As, in f(x), coefficient of x^4 is +ve, therefore, the function f(x) is monotonically increasing for x > 3h

After intersection with X ...

#### Solution Summary

In this solution, we find the point(s) within a given interval where a polynomial function may possibly have local maximum value (maxima). We estimate maximum value of the function at the point.

$2.19