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Show that f(x) = (k-(1)/(k)-x)(4-3x^(2))...

Show that `f(x) = (k-(1)/(k)-x)(4-3x^(2))` where k is a positive constant, has one and only one maximum value and only one minimum value and their difference is `(4)/(9)(k+(1)/(k))^(3)`

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The correct Answer is:
`4/9(k+1/k)^3`
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AAKASH SERIES-MAXIMA & MINIMA-EXERCISE-7.1
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  2. Find the intervals in which the following functions are stricly increa...

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  3. Find the intervals in which the following functions are stricly increa...

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  4. Find the intervals in which the following functions are stricly increa...

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  5. Find the intervals in which the following functions are stricly increa...

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  6. Find the intervals in which the following functions are stricly increa...

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  7. Find the intervals in which the following functions are stricly increa...

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  8. Determine the intervals in which f(x)=2/((x-1))+18x,AAx in R-{0} is st...

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  9. Let f(x)=sinx-cosx be defined on [0,2pi]. Determine the intervals in w...

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  10. Find all the points of local maxima and local minima of the function f...

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  11. Find the points at which the function f(x)=x^3-6x^2+9x+15 attain lo...

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  12. Find the points at which the function f(x)=-(x-1)^3(x+1)^2

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  14. Find the least and the greatest value of 2sin x + sin 2x over [0, 2pi]...

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  15. Find all local maximum and local minima of the sine function.

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  16. Show that f(x)=sin^(m)x.cos^(n)x has maximum value at x=Tan^(-1)sqrt(m...

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  17. Show that f(x) = (k-(1)/(k)-x)(4-3x^(2)) where k is a positive constan...

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