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Consider the function f(x)={{:(xsin(pi)/...

Consider the function `f(x)={{:(xsin(pi)/(x),"for"xgt0),(0,"for"x=0):}`
Then, the number of points in `(0,1)` where the derivative f'(x) vanishes is

A

0

B

1

C

2

D

infinite

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The correct Answer is:
D
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CENGAGE-APPLICATION OF DERIVATIVES-Exercise (Single)
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  7. The radius of the base of a cone is increasing at the rate of 3 cm/min...

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  8. If f(x)=x^3+7x-1, then f(x) has a zero between x=0a n dx=1 . The theor...

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  9. Consider the function f(x)={{:(xsin(pi)/(x),"for"xgt0),(0,"for"x=0):} ...

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  10. Let f(x)a n dg(x) be differentiable for 0lt=xlt=1, such that f(0),g(0)...

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  11. If 3(a+2c)=4(b+3d), then the equation a x^3+b x^2+c x+d=0 will have (a...

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  12. A value of c for which the conclusion of Mean value theorem holds for ...

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  13. Let f(x) be a twice differentiable function for all real values of x a...

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  14. The value of c in Lagranges theorem for the function f(x)=logsinx in t...

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  15. In which of the following function Rolle's theorem is applicable ?

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  16. Let f'(x)=e^(x)""^(2)and f(0)=10.If Altf(1)ltB can be concluded from t...

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  17. If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that ...

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  18. A continuous and differentiable function y=f(x) is such that its graph...

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  19. Given f^(prime)(1)=1"and"d/(dx)(f(2x))=f^(prime)(x)AAx > 0.If f^(pri...

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  20. If (x) is differentiable in [a,b] such that f(a)=2,f(b)=6, then there ...

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