Is #f(x)=(x-2)^2-6x-7 # increasing or decreasing at #x=-2 #?
1 Answer
Jan 28, 2016
Decreasing.
Explanation:
First, we should simplify
#f(x)=(x^2-4x+4)-6x-7#
#f(x)=x^2-10x-3#
To determine if the function is increasing or decreasing at
- If
#f'(-2)<0# , then the function is decreasing at#x=-2# . - If
#f'(-2)>0# , then the function is increasing at#x=-2# .
To find
#f'(x)=2x-10#
Determine the sign of the derivative:
#f'(-2)=-2(2)-10=-14#
Since this is
We can check a graph:
graph{x^2-10x-3 [-5, 15, -35.9, 50]}