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Let f((x+y)/(2))=1/2 |f(x) +f(y)|for all...

Let `f((x+y)/(2))=1/2 |f(x) +f(y)|`for all real x and y, if `f '(0)` exists and equal to `(-1), and f(0)=1 ` then `f(2)` is equal to-

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A DAS GUPTA-Differentiation-Exercise
  1. A function f is defined such that for all real x, y (a) f(x+y)=f(x).f(...

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  2. Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists. Prove that f'(...

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  3. Let f((x+y)/(2))=1/2 |f(x) +f(y)|for all real x and y, if f '(0) exist...

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  4. A function f(x) is so defined that for all real x,{f(x)}^n = f(nx). Pr...

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  5. Prove that the derivative of (a) an odd function is an even function;

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  6. Prove that the derivative of a periodic function of period T is a peri...

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  7. Let f(x) be a function satisfying the condition f(-x) = f(x) for all r...

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  8. A function f:R->R satisfies the relation f((x+y)/3)=1/3|f(x)+f(y)+f(0)...

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  9. Find the sum of series sum(r=1)^nr.x^(r-1), using calculus.

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  10. Differential coefficient of log2(log2x)w.r.t x is

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  11. If f(x)=logx(logex) then f'(e)=

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  12. If x=a (cos t +log (tan ((t)/(2)) )) ,y =a sin t ,then (dy)/(dx) =

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  13. Let f'(x) = sin(x^2) and y = f(x^2 +1) then dy/dx at x=1 is

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  14. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

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  15. If f'(x)=sin x^2 and y=f(x^2+1) then dy/dx=

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  16. If x=cost , y=loget then at t=pi/2, (d^2y)/(dx^2)+((dy)/(dx))^2=

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  17. If tany = (2t)/(1-t^2) and sin x = (2t)/(1+t^2) then (dy)/(dx)=

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  18. If xe^(xy)=y+sin^2x then at x=0 (dy)/dx=

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  19. If x^2y +y^3=2, the value of (dy)/(dx) at the point (1,1) is

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  20. Let f(x)={(tan)pi/4+tanx}{(tan)pi/4+(tan)(pi/4-x)}and g(x)=x^2+1. Then...

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