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Let f((x+y)/(2))= (f(x)+f(y))/(2) for al...

Let `f((x+y)/(2))= (f(x)+f(y))/(2)` for all real `x and y`. If `f'(0)` exits and equals -1 and `f(0) =1`, then find `f(2)`.

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The correct Answer is:
`f'(x) = -1`
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ARIHANT MATHS ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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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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  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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  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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  15. The domain of the derivative of the function f(x)={{:(tan^(-1)x ,if|x|...

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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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