On what interval does the function $f(x)=-\sin x$ increases and ....

Question

Can you explain me how do I find the intervals where the function:$$f(x)=-\sin x$$ is increasing and decreasing.

Thank you!

Answer 1

Check the derivative of $f(x)=-sinx$

$f^{'}(x)=-cosx$

Are you getting somewhere.

Answer 2

What is the derivative of $f$? By definition, the intervals for which $f'$ is positive will be the same intervals for which $f$ is increasing. Similarly, when $f'$ is negative, then $f$ is decreasing.

Hopefully this helps, but it really helps us help you when you provide us with as much background as possible. For example, useful information includes whether you know calculus, what you've tried, and where you are getting stuck.

If you do not know calculus, I recommend first trying to sketch the graph of $\sin(x)$ with help from the unit circle. Then, the negative will reflect the graph over the $y$-axis (why?).

Answer 3

here is the image of -sin(x)

and here is the image of -cos(x) which is the derivative of -sin(x)

compare the interval of -cos(x) is positive and the interval -sin(x) increase, compare the interval of -cos(x) is negative and the interval -sin(x) decrease. I hope it helps.