Find the interval in which the following function is strictly incerasing or decreasing,

$6 - 9 x - x^{2}$

Open in App

Solution

Given, $f (x) = 6 - 9 x - x^{2} \Rightarrow f^{'} (x) = - 9 - 2 x$
On putting, $f (x) = 6 - 9 x - x^{2} \Rightarrow f^{'} (x) = - 9 - 2 x$
On putting f'(x)=0, we get $- 9 - 2 x = 0 \Rightarrow x = - \frac{9}{2}$
Which divides the real line in two disjoint
intervals $(- \infty, \frac{- 9}{2})$ and $(- \frac{9}{2}, \infty)$

$\begin{matrix} I n t e r v a l s & S i g n o f f^{'} (x) & N a t u r e o f f (x) (- \infty, - \frac{9}{2}) & + v e & S t r i c t l y i n c r e a s i n g (- \frac{9}{2}, \infty) & - v e & S t r i c t l y d e c r e a s i n g \end{matrix}$
Therefore, f(x) is strictly increasing when $x < - \frac{9}{2}$ and strictly decreasing when $x > - \frac{9}{2}$ .

Suggest Corrections

Similar questions

Find the interval in which the following functions are strictly incerasing or decreasing

$10 - 6 x - 2 x^{2}$

Find the interval in which the following function is strictly incerasing or decreasing

$- 2 x^{3} - 9 x^{2} - 12 x + 1$

Find the interval in which the following function is strictly incerasing or decreasing,

$(x + 1)^{3} (x - 3)^{3}$

Find the interval in which the following functions are strictly incerasing or decreasing

$x^{2} + 2 x - 5$

$10 - 6 x - 2 x^{2}$

$- 2 x^{3} - 9 x^{2} - 12 x + 1$

$6 - 9 x - x^{2}$

$(x + 1)^{3} (x - 3)^{3}$

x^{2} + 2 x - 5

Join BYJU'S Learning Program