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Show that the function f(x)=(x-a)^2(x-b)...

Show that the function `f(x)=(x-a)^2(x-b)^2+x` takes the value `(a+b)/2` for some value of `x in [a , b]dot`

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The correct Answer is:
`f(c) = (a+b)/(2)`
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ARIHANT MATHS ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Show that the function f(x)=(x-a)^2(x-b)^2+x takes the value (a+b)/2 f...

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  2. about to only mathematics

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  3. Let f: R to R and g:R to R be respectively given by f(x) =|x|+1 and g...

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  4. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

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  5. Q. For every integer n, leta(n) and b(n) be real numbers. Let functio...

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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.

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  7. if f(x) ={{:(-x=(pi)/(2),xle -(pi)/(2)),(- cos x, -(pi)/(2)lt x ,le 0...

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  8. For the function f(x)=x cos ""1/x, x ge 1 which one of the following i...

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  9. Let g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2 m and n integers, m ne0...

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  10. Let fandg be real valued functions defined on interval (-1,1) such tha...

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  11. In the following, [x] denotes the greatest integer less than or equal ...

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

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  13. Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/a...

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  14. lf is a differentiable function satisfying f(1/n)=0,AA n>=1,n in I, th...

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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(pix) at x = k, k in Z, is

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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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