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Find critical points of f(x) =max (sinx ...

Find critical points of f(x) =max (sinx cosx) `AA , X in (0, 2pi)`.

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From the figure it is clear that f(x) has three critical points `X =(pi)/(4),(pi)/(2),(5pi)/(4),`
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RESONANCE-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. Find critical points of f(x) =max (sinx cosx) AA , X in (0, 2pi).

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  2. Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

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  3. f: [0.4]-> R is a differentiable function. Then prove that for some a,...

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  4. if all the function f(x)=a^2x^3-a/9x^2-2x-b arepositive and the minimu...

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  5. if f(x) = {underset(a^(2) -2+ (sin (x-K))/(x-K))(3+|x-k|)," "underse...

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  6. The equation x^3-3x+[a]=0, where [*] denotes the greatest integer func...

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  7. Let f(x) =sin ({x})/(a) + cos ({x})/(a) where a gt 0 and {.} denotes t...

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  8. Consider the equation x^4+4x^3-8x^2+K=0. Answer the following (1) Th...

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  9. A function f(x) having the following properties, (i) f(x) is conti...

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  10. A figure is bounded by the curves y=x^2+1, y=0,x=0,a n dx=1. At what p...

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  11. If y=(a x+b)/((x-1)(x-4)) has a turning value at (2,\ -1) find a\ &...

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  12. if A be the area of a triangle, prove that the error in A resulting fr...

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  13. Find the possible values of 'a' such that the inequality 3-x^(2)gt ...

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  14. lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1,then prove that...

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  15. find the interval of increasing and decreasing for the function g...

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  16. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

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  17. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

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  18. For any acute angled DeltaABC find the maximum value of (sin A)/(A) +(...

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  19. For what real values of a' and 'b' all the extrema of the function f(x...

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  20. Find the minimum value of f(x) =8^(x) +8^(-x) -4(4^(x)+4^(-x)) , AA x ...

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  21. Show that height of the cylinder of greatest volume which can be insc...

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