Question

If `f(x)=-(x-4)^2-3`, on what interval(s) is `f(x)` increasing?

Answer 1

(-infinity, 4)

Explanation:

To know where f(x) is increasing then we need to see where the derivaitve is +

f'(x)= `-2(x-4)`
This hits 0 at x=4
For x<4: the derivative is positive therefore the function is increasing.

For x>4: the derivative is negative therefore decreasing.

So for (-infinity, 4) the function is increasing.

Answer 2

`(-oo,4)`

Explanation:

To determine the interval that f(x) is increasing.

`• " increasing when " f'(x) > 0`

`f'(x)=-2(x-4)larrcolor(red)" using chain rule"`

`"solve " -2(x-4)> 0`

`rArr-2x+8>0`

`rArrx<4`

`" interval is " (-oo,4)`
graph{-(x-4)^2-3 [-8.89, 8.89, -4.445, 4.44]}