Find the intervals in which the following functions are strictly increasing or decreasing:
6 – 9x – x²

Question

Find the intervals in which the following functions are strictly increasing or decreasing: 6 – 9x – x 2

Philoid · Accepted Answer

It is given that function f(x) = 6 – 9x – x²

f’(x) = -9 – 2x

If f’(x) = 0, then we get,

⇒ x =

So, the point x = divides the real line into two disjoint intervals,

So, in interval

f’(x) = -9 – 2x > 0

Therefore, the given function (f) is strictly increasing for x < .

And in interval

f’(x) = -9 – 2x < 0

Therefore, the given function (f) is strictly decreasing for x>.

Thus, f is strictly decreasing for x>.

Find the intervals in which the following functions are strictly increasing or decreasing:6 – 9x – x2