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Answer with reasons, whether the followi...

Answer with reasons, whether the following function has a relative (local) maximum at x = 2 or not.
`f(x) = {{:(x,0 le x lt 1),(1,1 le x le 2),(3-x,2 lt x le 3):}`

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The correct Answer is:
.Hence, f(x) has no relative (local) maxima at x=2.
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ARIHANT PRAKASHAN-APPLICATION OF DERIVATIVES-TOPIC-2 (PRACTICE QUESTIONS) (1 MARK Questions)
  1. Mention the values of x for which the function f(x)= x^2 - 12x is incr...

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  2. Write the value of df, if f(x) = ln (1 + x), x = 1 and &x=0.04.

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  3. Write the set of points, where the function f(x) = x^(3) has relative ...

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  4. Answer with reasons, whether the following function has a relative (lo...

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  5. Find an approximate value of sqrt(16.04) using differential.

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  6. In which sub-interval of (0,(pi)/(2)) is x + 2 cos x increasing?

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  7. Write df, when f(x) = sqrt(x), x = 4 and Delta x = 0.2.

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  8. Find approximately the difference between the volumes of two cubes of ...

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  9. Determine the interval in which g(x) = (x^2+3x+3)/(x+1) is decreaing.

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  10. Determine the sub-interval of (-(pi)/(2),(pi)/(2)),in which f(x)= tan...

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  11. Using differential, find approximately the difference between the volu...

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  12. Prove that, if f(x) = a(0) + a(1)x^(2) + a(2)x^(4) and 0 lt a(0) lt a(...

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  13. Find the open interval in which f(x)= x^(1/x), x > 0 is decreasing.

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  14. Find the intervals where function is increasing function y = cos x + s...

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  15. Write the subinterval of (0,pi) in which sin (x+pi/4) is increasing.

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  16. Find the extreme points of the following functions. Specify if the ext...

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  17. For what value of x, is the function f(x) = 3 - 2x^2 the maximum?

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  18. What is the interval, in which y = x^2 + 2x + 3" "x epsilon R is decre...

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  19. Write the point, where f(x) = x log x attains minimum value.

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  20. Find delta f and df when f(x) = 2x^2 - 1, x = 1, delta x = 0 cdot 02

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