The Mean Value Theorem

a. Show that decreases on every interval in its domain.

b. How many solutions does the equation have? Give reasons for your answer.

Step 1 of 6:

a)In this problem, we need to show that decreases on every interval in its domain.

Step 2 of 6:

Given function is:

Now differentiate on both sides with respect to t we get.

, since

Therefore, …….(1)

Step 3 of 6:

We know that, sin(x) lies between [-1,1].

So, .

Therefore, .

is always falling.

Therefore, decreases on every interval in its domain.