Let f x - left matrix x - a- -if - X geq 1 ax - 2-1- - if - x -1end matrix right- - then f x is differentiable at x -1 ifA- a -1B- a -0C- a -2D- a -1 - 2

The correct option is D a=1/2 f^1(^ 1 )=f^1(1^+)⇒ 1=2a⇒ a=1/2 ...

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Byju's Answer

Standard XII

Mathematics

Local Maxima

Let f x = lef...

Question

Let $f (x) = {\begin{matrix} x + a, & i f x \geq 1 a x^{2} + 1, & i f x < 1 \end{matrix}$ , then f(x) is differentiable at x = 1 if

a=1

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a=0

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a=2

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a=1/2

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Solution

The correct option is D
a=1/2

$f^{1} (^{-} 1 -) = f^{1} (1^{+}) \Rightarrow 1 = 2 a \Rightarrow a = \frac{1}{2}$

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