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Verify Rolle's theorem for f(x)=x^3(x-1)...

Verify Rolle's theorem for `f(x)=x^3(x-1)^2` in the interval `0lexle1`

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PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. Prove that the curve (x/a)^n+(y/b)^n=2 touches the straught line x/a+y...

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  2. Prove that all points of the curve y^2=4a[x+asinx/a] at which the lang...

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  3. Verify Rolle's theorem for f(x)=x^3(x-1)^2 in the interval 0lexle1

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  4. If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

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  5. The value of 'c' of Rolls's throrem is applicable to the function f(x)...

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  6. Find 'c' of the Lagrange's mean value theorem for the function f(x)=3x...

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  7. If A(x1,y1) an B(x2,y2) be two points on the curve y=ax^2+bx+c then La...

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  8. 0 < a < b < ( pi/2​) and f(a,b)= (tanb−tana)/b-a

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  9. Let f,[2,7]rarr[0,oo) be a continuous and differentiable function, The...

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  10. If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p))...

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  11. If y=|cosx|+|sinx|,then(dy/dx)"at"x=(2pi)/3 is

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  12. The differential coefficient of f(logex) with respect to x, where f(x)...

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  13. If f(x) = cosx. cos2x. Cos4x. Cos8x.cos16x, then f '(pi/4) is :

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  14. If f(x)=log|2x|,x!=0 then f'(x) is equal to

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  15. The derivative of an odd function is always

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  16. If y=1/(1+x+x^2+x^3), then value of (d^2y)/(dx^2)at x=0 is

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  17. The function f(x)=(cosx+isinx)(cos3x+isin3x)...{cos(2n-1)x+isin(2n-1)x...

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  18. If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to

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  19. If x^3y^9=(x+y)^k and x(dy)/(dx)=y then k =

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  20. If y=log(3x+5) and (d^2y)/(dx^2)=A/(3x+5)^2 then A =

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