Question

f(x) = sinx is decreasing about $x=\pi$.

• A. True
• B. False

Answer 1

The correct option is A

True

As we saw, a function is decreasing at a point x = a, if it is decreasing in the neighborhood. So, we will find the value of the function at x = a-h, a and a+h. If we get a relation

f(a-h) $\ge$ f(a) $\ge$ f(a+h), then we say that the function is decreasing at x = a. This could be lengthy.

Instead, if we have f’(a) $\le$ 0, we can say that the function is decreasing about x =a.

So, we will find f’( $\pi$ ) to check if the function is decreasing about x = $\pi$

f’(x) = cos(x)

f’( $\pi$ ) = cos ( $\pi$ ) = -1

Which is negative. So we can clearly say that the function is decreasing about x = $\pi$.