A differentiable function is defined analytically by a)
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A differentiable function is defined analytically by
a) f(x)=x4e−0.5x.
Throughout this problem, numerical answers must be reported to at least three decimal places.
(a) Approximate f′(1.2). Show all supporting work, including intermediate calculator displays or computations that lead to your final value.
(b) Explain what the sign and magnitude of the value found in part (a) indicate about the instantaneous rate of change of f with respect to x at x=1.2. Your explanation should explicitly reference whether f is increasing or decreasing and describe the steepness of the graph at that point.