The function f(x)=6−6x−2x2
To find where the function increases or decreases, find the derivative:
f′(x)=−6−4x
The critical point occurs when f′(x)=0:
−6−4x=0
−4x=6
x=−23
For x<−23, test x=−2:
f′(−2)=−6−4(−2)
f′(−2)=−6+8
f′(−2)=2>0
The function is increasing when x<−23.
For x>−23, test x=0:
f′(0)=−6−4(0)
f′(0)=−6<0
The function is decreasing when x>−23.
Therefore, the function is strictly decreasing for x>−23.
