Let f(x) = cases (1+x)^ 2 3 , & -2 x < 0 (3x-5)^2, & 0 x 2 cases Which one of the…
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let
f(x)={(1+x)32,(3x−5)2,−2≤x<00≤x≤2
Which one of the following statements is correct?
(a) f(x) is continuous at each point on [−2,2]
(b) f(x) is differentiable for all x in (−2,2).
(c) Rolle's Theorem is applicable for f(x) in [−2,2].
(d) There exists at least one c∈(−2,2) for which f′(c)=0