Let $$f(x)=1$$|x|, |x|≥$$1ax2+b$$,|x|<$$1$$ be continuous and differentiable every where then

Correct option is 1a=−1/2,b=3/2

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$Let f (x) = \{\begin{cases} \frac{1}{| x |}, | x | \geq 1 \\ a x^{2} + b, | x | < 1 \end{cases} be continuous and differentiable every where then$

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a=−1/2,b=3/2

a=1/2,b=−3/2

a=1/2,b=3/2

a=−1/2,b=−3/2

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detailed solution

Correct option is A

f(x)=1|x|, |x|≥1ax2+b,|x|<1 f is continuous at x=1 a+b=1 f1(x)=-1x2, |x|≥12ax, |x|<1 2a=-1⇒a=-12, b=32

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Let f(x)=1|x|, |x|≥1ax2+b,|x|<1 be continuous and differentiable every where then

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Ready to Test Your Skills?

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$Let f (x) = \{\begin{cases} \frac{1}{| x |}, | x | \geq 1 \\ a x^{2} + b, | x | < 1 \end{cases} be continuous and differentiable every where then$