Let . If is the continuous and differentiable for all numbers in its domain,…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let g(x)={3x2−4x+1,for x<1ax+b,for x≥1g(x) = \begin{cases} 3x^2 - 4\sqrt{x} + 1, & \text{for } x < 1 \\ ax + b, & \text{for } x \ge 1 \end{cases} . If g(x)g(x) is the continuous and differentiable for all numbers in its domain, then (1) a=b=4a = b = 4 (2) a=b=−4a = b = -4 (3) a=4a = 4 and b=−4b = -4 (4) a=−4a = -4 and b=4b = 4

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