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If the derivative of the function f(x)...

If the derivative of the function
`f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+ax+4,xge-1):}`
is every where continuous, then what are the values of a and b?

A

a=2,b=3

B

a=3, b=2

C

a=-2, b=-3

D

a=-3, b=-2

Text Solution

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The correct Answer is:
A
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. A function is defined as follows : f(x) = {{:(x^(3), x^(2) lt 1),(x,...

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  2. The left-hand derivative of f(x) =[x]sin (pix) at k an interger, is:

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  3. If the derivative of the function f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+a...

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  4. If f(x) = {{:(ax^(2) + b, b ne 0, x le 1),(bx^(2) + ax + c,, x gt 1):}...

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  5. Let f(x) = a|x|^(2) + b|x| +c where a,b,c are real constants. Then f'(...

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

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  7. Let f : R to R be a function defined by f(x) = max. {x, x^(3)}. The s...

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  8. The derivative of f(x) =|x| at x = 0 is:

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  9. For a differentiable function f, the value of lim(h to 0) ([f(x+h)]^(2...

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

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  11. The function f(x) = e^(|x|) is

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  12. Let f(x) be defined as f(x) = {{:(sin 2x, 0 lt x lt pi/6),(px + q, p...

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  13. Let f(x) = {{:(-1/|x|, "for " |x| ge 1),(ax^(2)-b, "for " |x| lt 1):},...

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  14. The derivative of f(x) =|x|^(3) at x=0 is:

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  15. If y=|tan (pi/4-x)|, then (dy)/(dx) at x=pi/4 is

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

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  17. f(x)=||x|-1| is not differentiable at

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  18. The number of points at which the function f(x) =|x-0.5|+|x-1| + tan x...

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  19. Consider, f(x) = {{:(x^(2)/(|x|), x ne 0),(0, x =0):}

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  20. The function f(x) = (x^(2)-1)|x^(2) -3x+2| + cos(|x|) is not differen...

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