MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f be continuous on [−5,3] and differentiable on (−5,3).
The derivative f′ satisfies the following:
• f′(x)>0 for −5<x<−1
• f′(−1)=0
• f′(x)<0 for −1<x<1
• f′(1)=0
• f′(x)>0 for 1<x<3
Additional function values are f(−5)=2,f(−1)=7,f(1)=1,f(3)=4.
At which x–value does f attain its absolute maximum on [−5,3]?
(a) x=3
(b) x=−1
(c) x=1
(d) x=−5