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

$(0, \frac{π}{2})$

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Solution

In interval $(0, \frac{π}{2}), c o s x > 0$ and $100 x^{99} > 0$
$∴ 100 x^{99} + c o s x > 0 \Rightarrow f^{'} (x) > 0$ in $(0, \frac{π}{2})$
Thus, f is strictly increasing in interval $(0, \frac{π}{2})$
Hence, function f is not strictly decreasing in the given intervals.

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Similar questions

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

$(\frac{π}{2}, π)$

f

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

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

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

(A) (B)

Show that the function given by $f (x) = s i n x$ is
strictly increasing in $(0, \frac{π}{2})$

strictly decreasing in $(\frac{π}{2}, π)$

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

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