On which of the following intervals, the function $x^{100} + sin x - 1$ is strictly increasing.

(- 1, 1)

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(0, 1)

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(π / 2, π)

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(0, π / 2)

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Solution

The correct options are
B $(0, 1)$
C $(0, π / 2)$
D $(π / 2, π)$
Let $f (x) = x^{100} + s i n x - 1$
$f^{'} (x) = 100 x^{99} + c o s x$
for $f (x)$ to be strictly increasing function
$f^{'} (x) > 0 \Rightarrow 100 x^{99} + c o s x > 0$
$\Rightarrow x \geq 0$
Hence option A, B, C are correct.

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Similar questions

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

(A) (B)

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.

$(0, \frac{π}{2})$

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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