Question

Test whether the given functions are increasing or decreasing f(x) = cos x 0 < x < π

Answer 1

Answer:

f(x) is decreasing in (0 , π)

Step-by-step explanation:

Concept used:

If $f(x)\geq\:0$ for all in I, then f(x) increasing in I

If $f(x)\leq\:0$ for all in I, then f(x) increasing in I

Given function is

f(x) = cos x

f'(x) = - sinx

For all x∈ (0 , π), Take x= π/2

f'(π/2) = - sin(π/2)= -1 < 0

This implies f'(x) < 0 for all x∈ (0 , π)

Hence, f(x) is decreasing in (0 , π)

Answer 2

Answer:

Decreasing function

Step-by-step explanation:

The function is f(x)= Cos x

We have to find this function increasing or decreasing in the interval, 0 < x < π.

We know that f(x) will be an increasing function if f'(x)>0 with in a said interval of x.

And f(x) will be a decreasing function if f'(x)<0 with in a said interval of x.

Now, f(x)= Cos x .....(1)

⇒f'(x) = -Sin x .....(2)

Now, we know that "Sin x" is positive for all values of x in the interval 0 < x < π.

So, f'(x) is always negative for all x in the interval  0 < x < π.

Therefore, we can conclude that the function f(x) is decreasing in this interval 0 < x < π.