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Let f: R to R be a function defined by :...

Let `f: R to R` be a function defined by :
`f(x)="Min".{x+1,|x|+1}`.
Then which of the following is true ?

A

`f(x)` is not differentiable at `x=1`

B

`f(x)` is differentiable everywhere

C

`f(x)` is not differentiable at `x=1`

D

`f(x)ge1` for all `x in R`.

Text Solution

Verified by Experts

The correct Answer is:
B
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MODERN PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -MCQs (LEVEL-II)
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  2. The function f(x)=(x^(2)-1)|x^(2)-3x+1|+cos(|x|) is not differentiable...

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  3. If y=ce^(x//(x-a)), then 1/y(dy)/(dx) is equal to :

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  4. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

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  5. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

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  6. Derivative of (log x)^(4) is

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  7. If x=e^(y+e^(y+ . . . . .. "to "oo)),xgt0, then (dy)/(dx) is :

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  8. Suppose f(x) is differentiable at x=1 and lim(hto0)(1)/(h)(1+h)=5, the...

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  9. If f is a real valued differentiable function satisfying : |f(x)-f(y...

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  10. If f(x)=||x|-1|, then it is non - derivable at :

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  11. If f:R to T is continuous and differentiable function such that f((1)/...

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  12. If xsiny+ycosx=pi, then the value of y''(0) is :

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  13. The set of points, where f(x)=(x)/(1+|x|) is differentiable, is :

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  14. If x^(m)y^(n)=(x+y)^(m+n), then (dy)/(dx)=

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  15. Let f(x) be differntiable on the interval (0,oo) such that f(1)=1 and ...

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  16. Let f: R to R be a function defined by : f(x)="Min".{x+1,|x|+1}. T...

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  17. Let f(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2,m and n are intgers, m!...

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  18. Let y be an implicit fuction of x defined by : x^(2x)-2x^(x) cot y-1...

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  19. Let f(x){{:((x-1)"sin"(1)/(x-1)", "ifx!=1),(" 0, ...

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  20. Let g(x)=log(f(x)), where f(x) is a twice differentiable positive func...

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