Let . (i) List all critical points of . (ii) Determine the sign of on each interval…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

h'(x)=(x-1)^{2}(x+2)(x-4)

. (i) List all critical points of

h

. (ii) Determine the sign of

h'(x)

on each interval defined by these critical points. (iii) Sketch a qualitative graph of

y=h(x)

that shows all turning points and indicates where the function rises and falls.