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If f(x) = alpha x^n, prove that alpha= (...

If `f(x) = alpha x^n`, prove that `alpha= (f'(1))/n` .

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. If f(x) =x^n and if f’ (1) = 10, find n.

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  2. Find a if f’ (a) =0, where f(x) =x^3- 3x^2 + 3x-1.

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  3. If f(x) = alpha x^n, prove that alpha= (f'(1))/n .

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  4. Prove from first principles, that d/(dx)(alpha x^n)=alpha nx^(n-1) .

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  5. Use the delta method to find the derivative of f (x) = x^4 .Hence find...

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  6. If y=1+(x)/(1!)+(x^(2))/(2!)+(x^(3))/(3!)+ . . .+(x^(n))/(n!), prove t...

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  7. Find the derivatives of the following function at any point of their d...

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  8. Find the derivatives of the following function at any point of their d...

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  9. Find the derivatives of the following function at any point of their d...

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  10. Find the derivatives of the following function at any point of their d...

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  11. Find the derivatives of the following function at any point of their d...

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  12. Find the derivatives of the following function at any point of their d...

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  13. Find the derivatives of the following function at any point of their d...

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  14. Find the derivatives of the following function at any point of their d...

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  15. Let f(x) = 3x^3 + 7x^5. Find f’ (2).

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  16. Let f(x) = x^3/3-x^2/2+x-16. Find f’(0), f’(-1).

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  17. Given u= 7t^4-2t^(3)-8t-5, find (du)/(dt). Hence, find (du)/(dt) at t...

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  18. Let H (y) =2y^4-6y^3+2y-4. Find H^(')(2).

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  19. Let G(u)=2-u^(3)+u^(5)/5. Find G^(')(-2).

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  20. If (x) = mx +c and if f(0)=f'(0)=1, what is f(2) ?

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