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Find the interval in which the function `f(x)= x^3-6x^2+9x+5` is decreasing.

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UNITED BOOK HOUSE-SET 5-EXERCISE
  1. Verify Rolle' theorem for the function f(x)= x^2-4x+3 in 1lexle3.

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  2. solve : (dy)/(dx) = (1-cos x)/(1+ cosx)

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  3. Find the interval in which the function f(x)= x^3-6x^2+9x+5 is decrea...

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  4. If vec a= 4 hati- hat j-3hat k and vec b = -2 hat i+hat j+2 hat k are ...

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  5. Find the equation of the plane passing through the point (4,1,1) and p...

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  6. The mean and standard deviationg of a binomial distribution B(n,p) ar...

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  7. The value 2tan^(-1)[sqrt((a-b)/(a+b))tan(theta/2)] is equal to cos^(-1...

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  8. If A = [[2,-1],[3,2]] and B = [[0,4],[-1,7]] then determine the matric...

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  9. If [1x1]xx[[1,3,2],[2,5,1],[15,3,2]]xx[[1],[2],[x]]=0 then find the va...

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  10. Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

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  11. If y = 2 sin^(-1)(x-2)/sqrt6-sqrt(2+4x-x^2), then show that (dy)/(dx)|...

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  12. If t is a parameter and x = t^2+2t,y = t^3-3t then show that (d^2y)/(d...

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  13. Evaluate :intdx/(3+2sinx+cosx)

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  14. Evaluate: int( (x-1)dx)/((x-3)(x-2))

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  15. Solve: (dy)/(dx)+y tan x= 2x+x^2 tanx

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  16. Solve: xdx + y dy + xdy - ydx = 0

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  17. If the position vector of A,B,C are 2i+4j-k,4i+5j+k and 3i+6j-3k respe...

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  18. Find a unit vector perpendicular to the plane of ABC where the positio...

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  19. Prove that overset(pi)underset(0)int (xdx)/(a^2 cos^2x +b^2 sin^2x) = ...

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  20. Prove that overset(3)underset(0)int(2x^2+3x+5)dx= 93/2

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