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Change of Variables

On which of t...

Question

On which of the following intervals is the function f given by strictly decreasing?

(A) (B)

(C) (D) None of these

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Solution

We have,

In interval

Thus, function f is strictly increasing in interval (0, 1).

In interval

Thus, function f is strictly increasing in interval.

∴ f is strictly increasing in interval.

Hence, function f is strictly decreasing in none of the intervals.

The correct answer is D.

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Similar questions

On which of the following intervals is the function f given by $f (x) = x^{100} + s i n x - 1$ strictly decreasing.

a) (0,1)

b) $(\frac{π}{2}, π)$

c) $(0, \frac{π}{2})$

d) None of these

Check whether the function f given by $f (x) = x^{100} + s i n x - 1$ strictly decreasing in the given interval.

$(\frac{π}{2}, π)$

Check whether the function f given by $f (x) = x^{100} + s i n x - 1$ strictly decreasing for the given interval.

$(0, \frac{π}{2})$

Q. On which of the following intervals is the function

f

f (x) = x^{100} + sin x - 1

strictly decreasing ?

Show that the function given by f(x) = sin x is

(a) strictly increasing in (b) strictly decreasing in

(c) neither increasing nor decreasing in (0, π)

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