MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let
f(x)=x2+35x+1.
Answer the following questions about f.
(a) Calculate f′(x) and simplify your result.
(b) Evaluate f′(2), expressing your answer as a simplified rational number.
(c) Interpret the meaning of the value found in part (b) as the instantaneous rate of change of f at x=2. State whether the function is increasing or decreasing at that point and support your claim numerically.