Question

Identify intervals on which the function is increasing, decreasing, or constant. G(x) = 1 - (x - 6)2

Answer 1

Answer: The function is increasing in the interval  $(-\infty, 6)$

And, decreasing in the interval  $(6,\infty)$

Step-by-step explanation:

Here, the given function,

$G(x) = 1 - (x - 6)^2$

On Differentiating the above equation with respect to x,

We get,

$G'(x) = - 2(x - 6)$

When   G'(x) =0,

$-2(x - 6) = 0$

$x - 6 = 0$

$x = 6$

In the interval $(-\infty, 6)$,   $G'(x) > 0$

Therefore, G(x) is increasing in the interval $(-\infty, 6)$.

Now, In the interval $(6,\infty)$,  $G'(x) < 0$

Therefore, G(x) is decreasing in the interval $(6,\infty)$.