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Let h(x)="min "{x,x^(2)} for every real ...

Let `h(x)="min "{x,x^(2)}` for every real number of x. Then, which one of the following is true?

A

h is not continuous for all x

B

h is differentiable for all x

C

`h'(x) = 1` for all x

D

h is not differentiable at two values of x

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The correct Answer is:
D
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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  6. Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R. a. ...

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  7. If f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)), (- cos x, -(pi)/(2)lt x ,le ...

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  11. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

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  12. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

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  13. Fill in the blank, in the statement given below. Let f(x) = x|x The ...

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  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

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  16. The left hand derivative of f(x) = [x] sin (pi x)"at x" = k is an inte...

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  17. Which of the following functions is differentiable at x = 0 ?

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  18. For x in R, f(x) =|log(e) 2-sinx| and g(x) = f(f(x)) , then

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  19. If the function g(X) ={{:( ksqrt ( x+1), 0 le x le 3),( mx+2, 3 lt x...

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  20. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  21. The function f(x) = [x] cos((2x-1)/2) pi where [ ] denotes the greate...

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