If f(x)=-(x-4)^2-3f(x)=(x4)23, on what interval(s) is f(x)f(x) increasing?

2 Answers
Apr 10, 2017

(-infinity, 4)

Explanation:

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

f'(x)= -2(x-4) 2(x4)
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.

Apr 10, 2017

(-oo,4)(,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]}