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Find the intervals of monotonocity for t...

Find the intervals of monotonocity for the following functions & represent your solution set on the number line.
Also plot the graph in each case.
`f(x)=2x^(2)-ln |x|`

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Verified by Experts

The correct Answer is:
I for `x gt 1/2` or `-1/2 lt x lt 0 & "D for " x lt - 1/2 ` or `0 lt x lt 1/2`
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MOTION-MONOTONOCITY-Exercise - 3 ( Subjective )
  1. Find the intervals of monotonocity for the following functions & repre...

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  2. Find the intervals of monotonocity for the following functions & repre...

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  3. Find the intervals of monotonocity for the following functions & repre...

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  4. Let f(x)={:{(x^(2),x ge 0),(ax, x lt 0):}. Find real values of a such...

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  5. If f(x) = x^(3) + (a – 1) x^(2) + 2x + 1 is strictly monotonically in...

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  6. Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x...

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  7. Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1)...

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  8. Using monotonicity prove that x lt - ln (1-x) lt x (1-x)^(-1) for ...

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  9. Using monotonicity prove that (x)/(1-x^(2)) lt tan^(-1)x lt x for...

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  10. Prove that tan^2x+6lns e c x+2cosx+4>6secx for x\ in ((3pi)/2,\...

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  11. Verify Rolles theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}...

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  12. Using Rolle's theorem prove that the equation 3x^2 + px - 1 = 0 has th...

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  13. f(x) and g(x) are differentiable functions for 0 le x le 2 such that ...

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  14. Show that the lagranges mean value theorem is not applicable to the...

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  15. If a, b are two real numbers with a lt b show that a real number 'c' ...

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  16. Using LMVT prove that : (a) tan x gt x in (0, pi/2), (b) sin x l...

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  17. Construct the graph of the function f(x)=-|(x^(2)-9)/(x+3)-x+(2)/(x-...

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  18. Show that exactly two real values of x satisfy the equation x^2= xsinx...

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  19. If g(x) is monotonically increasing and f(x) is monotonically decreasi...

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  20. For x in (0, pi/2) identify which is greater (2 sin x + tan x ) or ...

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