Consider the function h(x) = (4x - 1)(x^2 + 2x + 1) x^3 - 5
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider the function
h(x)=x3−5(4x−1)(x2+2x+1),x3=5.
Respond to the following.
(a) Derive an expression for h′(x) and simplify the numerator as much as possible.
(b) Show that the simplified numerator obtained in part (a) is divisible by x2+2x+1.
(c) Using the result of part (b), evaluate h′(1).