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