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Let f(x)={{:(,x^(3),x lt 1),(,ax^(2)+bx+...

Let `f(x)={{:(,x^(3),x lt 1),(,ax^(2)+bx+c,:x ge 1):}`. If f''(1) exists, then the value of `(a^(2)+b^(2)+c^(2))` is

A

20

B

21

C

19

D

17

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OBJECTIVE RD SHARMA-CONTINUITY AND DIFFERENTIABILITY-Exercise
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  9. Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and...

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  10. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

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  11. Let f(x+y)=f(x) f(y) and f(x)=1+(sin 2x)g(x) where g(x) is continuous....

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  12. Let g(x) be the inverse of an invertible function f(x) which is differ...

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  13. Let g(x) be the inverse of the function f(x), and f'(x)=1/(1+x^3) then...

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  14. Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is conti...

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  15. If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e...

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  16. Let f(x) be a function such that f(x+y)=f(x)+f(y) and f(x)=sin x g(x)...

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  17. Let f(0,pi) to R be defined as f(x)={{:(,(1-sinx)/((pi-2x)^(2)).(In si...

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  18. If f(x)=(e^(2x) - (1+4x)^(1//2))/(ln(1-x^2)) for x != 0, then f has

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  19. Let f(x)={{:(,(e^(x^2)-(2)/(pi)sin^(-1)sqrt(1-x))/(In(1+sqrtx)),x in (...

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  20. Let f(x)={{:(,x^(3),x lt 1),(,ax^(2)+bx+c,:x ge 1):}. If f''(1) exists...

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