Question

Find and classify the critical points of
f(x)=x^3(1-x)^4 as local maxima and minima.

Answer 1

Critical points are possible points of extrema (maxima/minima). To determine critical points for a polynomial function

i). Find the derivative and set it equal to zero to solve for x. The x values are your critical numbers.
ii). For each x, find the corresponding y value. These y values are your critical values.