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If `f (x-y), f (x) ,f (y) and f (x + y) ` are in A.P for all x,y `in E and f (0) = 0` show that `f ' (x)` is even.

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AAKASH SERIES-DIFFERENTIATION -ADVANCED SUBJECTIVE TYPE QUESTIONS
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  2. The number of cirtical points of the function f(x)=|x|e^(-x) must be

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  3. If f (x-y), f (x) ,f (y) and f (x + y) are in A.P for all x,y in E an...

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  4. Let f : R to R be a function defined by f (x + y) = f (x).f (y) and f ...

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  5. If f (x +y) = 2 f (x) .f(y) such that f '(0) 3 and (4) = 2 find d'(4)...

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  6. Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x,...

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  7. If f (x) is a function such that (x - y) f (x + y)- (x + y) f (x - y) ...

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  8. Show that (d ^(2)x)/( dy^2) =- ((d ^(2) y )/( dx ^(2))) ((dy)/(dx)) ^(...

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  9. If f (x) = {{:((x ^(2))/( 2 ) "," , 0 le x lt 1), (2x ^(2) - 3x + (3)/...

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  10. Show that the function f (x) = |x-1|+ | x- 2| is not differentiable at...

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  11. Prove theat the greatest interger function defined by f(x)= |x|, 0 lt ...

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  12. Show that the function f (x) = {{:( x, if x lt 1), ( 6 -2x , if 1 le x...

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  13. If 'f is a function such that f (x + y) =f (x) f (y) for all x,y in R ...

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  14. If f (x) = ax ^(2) + bx + c then find Lt (x to 5) (f (x) - f (5))/(x-...

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  15. If f (x) has a derivative at x =a then find Lt (x to a) (x f (a) - a f...

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  16. Prove that f (x) = x |x| is differentiable at x =0 and find f'(0) als...

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  17. Show that the function f (x) = (x)/(1 + |x| ) , x in R, is differentia...

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  18. Show that the functions f (x) = x ^(3) sin ((1)/(x)) for x ne 0, f (0)...

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  19. If f (x) = (x -1)/( 2x ^(2) - 7x + 5) for x ne 1, f (1) = (-1)/(3), fi...

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  20. For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+….+(x^(2))/(2)+x...

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