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Show that the function f given by f(x) =...

Show that the function f given by `f(x) = tan^-1(sinx+cosx), x>0` is always an increasing function in `f, (0,pi/4)`

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Prove that the function f(x) = tanx-4x is strictly decreasing on (-pi/...

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  2. Find the interval in which the function f(X) = x^4 - (4x^3)/(3) is str...

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  3. Show that the function f given by f(x) = tan^-1(sinx+cosx), x>0 is alw...

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  4. State whether the function f(x) = x^3 is increasing or decreasing.

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  5. State whether the function f(x) = e^x is increasing or decreasing.

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  6. Is the function y = cot x decreasing on the interval (0,pi)?

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  7. Find the interval of increase of the function f(x) = tan^-1 x.

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  8. Find the interval of decrease of the function f(X) = sin x - 2x

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  9. Find the interval of increase of the function f(x) = 3x + cos x

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  10. Find the slope of the tangent to the curve y = 3x^2 at the point (1/6,...

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  11. For the curve y = 5x - 2x^3, if x increases at te rate of 2units/s, th...

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  12. Find the slope of the normal to the curve y = x^3 at the point whose a...

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  13. At what point on the curve y = x^2 - 2x, the tangent is parallel to x-...

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  14. At what point on the curve y = 2x^2 - 4x + 3, the normal is parallel t...

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  15. Find the slope of the normal to the curve y = 1/x at the point (1/3,3...

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  16. Find the equation of the tangent to the curve y = x^2 - x + 2 where it...

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  17. Find the change in the value of y=x^2 when x = 10 and Deltax = 0.01

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  18. Find the approximate volume of metal in a hollow spherical shel, whose...

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  19. Find the maximum value of sin x cos x.

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  20. Find the maximum vlaue (1)/(x^2 + x + 1), x in R

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