On which of the following intervals is the function $x^{100} + sin x - 1$ decreasing?

(0, \frac{π}{2})

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(0, 1)

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(\frac{π}{2}, π)

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None of the above.

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Solution

The correct option is D None of the above.
The given equation : $f (x) = x^{100} + sin x - 1$
$f^{1} (x) = 100 x^{99} + cos x - 0$
$f^{1} (x) = 100 x^{99} + cos x$
$E q u a t e f^{1} (x) = 0$
$100 x^{99} + cos x = 0$
$100 x^{99} = - cos x$
The domain of a function is set of inputs for which the function is real and defined
The function increasing in the range $(- \infty, \infty)$

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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.

$(0, \frac{π}{2})$

(0, π / 2)

(0, π / 2)

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