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in Continuity and Differentiability by (29.1k points)
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Let \(f(x) = \begin{cases} ax^2+1 &, x>1 \\ x+\frac{1}{2} & , x \leq 1 \end{cases},\) Then, f(x) is derivable at x = 1, is

A. a = 2

B. a = 1

C. a = 0

D. a = 1/2

1 Answer

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by (28.7k points)
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Best answer

Correct answer is D.

Given function \(f(x) = \begin{cases} ax^2+1 &, x>1 \\ x+\frac{1}{2} & , x \leq 1 \end{cases}\) and f(x) is derivable at x = 1.

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