Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABhardmcq1 pt

Find the values of aa and bb so that f(x)={x2−4x+5,x≤2ax+b,x>2f(x)=\begin{cases} x^2-4x+5, & x\le 2 \\ ax+b, & x>2 \end{cases} is differentiable at x=2x=2.

A.a=0a=0, b=1b=1
B.a=0a=0, b=5b=5
C.a=1a=1, b=1b=1
D.a=2a=2, b=−3b=-3

Explanation

Core Concept

The left piece gives f(2)=1f(2)=1 and slope f′(2)=2(2)−4=0f'(2)=2(2)-4=0. The right piece must match: 2a+b=12a+b=1 and a=0a=0, so b=1b=1.

Correct Answer

Aa=0a=0, b=1b=1

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