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Find the values of x for which y = [x(x ...

Find the values of x for which y = `[x(x – 2)]^(2)` is an increasing function.

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The correct Answer is:
y(x) is increasing in `(0,1) and (2, oo)`.
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SUBHASH PUBLICATION-APPLICATION OF DERIVATIVES -THREE MARKS QUESTIONS WITH ANSWERS (A) DECREASING AND INCREASING FUNCTIONS
  1. Find the intervals in which the function f given by f(x) = 2x^(2) - 3x...

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  2. Find the intervals in which the function f given by f(x) = 2x^(3) - 3x...

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  3. Find the intervals in which the functions f given by f(x) = 4x^(3) - 6...

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  4. Show that the function given by f(x) = sin x is (a) strictly increas...

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  5. Show that the function given by f(x) = sin x is (b) strictly decreas...

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  6. Show that the function given by f(x) = sin x is (c) neither increasi...

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  7. Prove that the function given by f(x) = cos x is (a) strictly decrea...

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  8. Prove that the function given by f(x) = cos x is (b) strictly increa...

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  9. Prove that the function given by f(x) = cos x is (c) neither increas...

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  10. Find the intervals in the function f is given by f(x) = sin x + cos x,...

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  11. Find the interval in which the following functions are strictly increa...

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  12. Find the interval in which the following functions are strictly increa...

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  13. Find the interval in which the following functions are strictly increa...

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  14. Find the interval in which the following functions are strictly increa...

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  15. Find the interval in which the following functions are strictly increa...

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  16. Show that y = log(1 +x) - (2x)/(2 + 2x) , x gt -1, is an increasing fu...

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  17. Find the values of x for which y = [x(x – 2)]^(2) is an increasing fu...

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  18. Prove that y = (4 sin theta)/((2 + cos theta)) - theta is an increasin...

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  19. Prove that the logarithmic function is strictly increasing on (0, oo).

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

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