MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
Let h(x)=(2x−1)x for x>0. The graph of h is shown in the xy–plane.
(a) Derive an explicit expression for h′(x). Show all algebraic steps.
(b) Evaluate h′(4) and state its numerical value.
(c) Determine the equation of the tangent line to the graph of h at x=4, writing your final answer in point–slope form.
(d) Use the tangent line found in part (c) to approximate h(4.2). Clearly indicate the value obtained and the substitution used.