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Let f(x) ={underset(x^(2) +nb " " x g...

Let f(x) `={underset(x^(2) +nb " " x ge1)(3-x " "0le x lt1).` Find the set of values of b such that f(x) has a local minima at x=1.

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The correct Answer is:
`b in (0 , e]`
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MOTION-MAXIMA AND MINIMA -EXERCISE - 3
  1. Find the points of local maxima/minima of function f(x) = x ln x

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  2. Let f(x) = {{:( 2 sin x ,, x gt 0) , ( x^(2) ,, x le 0):} . Investigat...

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  3. Find the number of critical points of the function f (x) = - (3)/(4...

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  4. Find the number of critical points of the function f(x) = |x - 2| +...

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  5. Find the number of critical points of the function f (x) = min (tan...

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  6. Let f (x) = x^(2) , x in [-1 , 2) Then show that f(x) has exactly one ...

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  7. Let f (x) = x + sqrtx . Find the greatest and least value of f(x) for ...

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  8. Let f(x) ={underset(x^(2) +nb " " x ge1)(3-x " "0le x lt1). Find ...

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  9. Find the points of local maxima/minima of following functions (i) f ...

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  10. Show that sin^(p) theta cos^(q) theta , p , q in N attains maximum val...

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  11. A telephone company in a town has 500 subscribers on its list and c...

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  12. A factory D is to be connected by a road with a straight railway line ...

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

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  14. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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  15. Draw graph of f(x) =x|x-2| and hence find points of local maxima//mini...

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  16. The exhaustive set of value of 'a' for which the function f(x)=a/3(x...

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  17. Find the polynomial f(x) of degree 6, which satisfies underset(x to 0...

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  18. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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  19. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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  20. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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