Q

# Find the intervals in which the following functions are strictly increasing or decreasing 10 - 6x -2 x ^2

6) Find the intervals in which the following functions are strictly increasing or
decreasing

b) $10 - 6x - 2x^2$

Views

Given function is,
$f(x) = 10 - 6x - 2x^2$
$f^{'}(x) = -6 - 4x$
Now,
$f^{'}(x) = 0$
$6+4x= 0$
$x= -\frac{3}{2}$

So, the  range is $(-\infty , -\frac{3}{2}) \ and \ (-\frac{3}{2},\infty)$
In interval $(-\infty , -\frac{3}{2})$  ,  $f^{'}(x) = -6 - 4x$ is +ve
Hence, $f(x) = 10 - 6x - 2x^2$ is strictly increasing in the interval  $(-\infty , -\frac{3}{2})$
In interval $( -\frac{3}{2},\infty)$  , $f^{'}(x) = -6 - 4x$ is -ve
Hence, $f(x) = 10 - 6x - 2x^2$ is strictly decreasing in interval  $( -\frac{3}{2},\infty)$

Exams
Articles
Questions