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Prove that the logarithmic function is i...

Prove that the logarithmic function is increasing on `(0,∞)`.

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PSEB-APPLICATION OF DERIVATIVES-Exercise
  1. Find the values of x for which y = [x(x-2)]^2 is an increasing functio...

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  2. Prove that y = 4sin theta/(2 + cos theta) - theta, is an increasing fu...

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  3. Prove that the logarithmic function is increasing on (0,∞).

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  4. Prove that the function f given by f(x) = x^2-x+1 is neither strictly ...

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  5. Which of the following functions are strictly decreasing on ( 0, pi/2 ...

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  6. On which of the following intervals is the function f given by f(x) = ...

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  7. For what values of a the function f given by f(x) = x^2 +ax + 1 is inc...

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  8. Let I be any interval disjoint from [-1,1] Prove that the function f g...

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  9. Prove that the function f given by f(x) = log sinx, is increasing on (...

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  10. Prove that the function f given by f(x) = log |cosx| is decreasing on ...

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  11. Prove that the function given by f(x) = x^3 - 3x^2 + 3x - 100 is incre...

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  12. The interval in which y = x^2 e^-x is increasing is:

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  13. Find the slope of the tangent to the curve y = 3x^4-4x at x= 4

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  14. Find the slope of the tangent to the curve y = (x-1)/(x-2) at x = 10.

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  15. Find the slope of the tangent to curve y = x^3-x+1 at the point whose ...

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  16. Find the slope of the tangent to the curve y = x^3-3x+2 at the point w...

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  17. Find the slope of the normal to the curve x = a cos^3 theta, y = a sin...

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  18. Find the slope of the normal to the curve x = 1 - a sin theta, y = b c...

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  19. Find points at which the tangent to the curve y = x^3-3x^2-9x+7 is par...

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  20. Find a point on the curve y = (x - 2)^2 at which the tangent is parall...

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