Is #f(x)=x^23x # increasing or decreasing at #x=2 #?
1 Answer
Jan 28, 2016
Decreasing.
Explanation:
The sign (positive/negative) of the first derivative of a function tells if the function is increasing or decreasing at a point.

If
#f'(2)<0# , then#f(x)# is decreasing at#x=2# . 
If
#f'(2)>0# , then#f(x)# is increasing at#x=2# .
To find the derivative of the function, use the power rule.
#f(x)=x^23x#
#f'(x)=2x3#
Find the sign of the derivative at
#f'(2)=2(2)3=7#
Since
We can check by consulting a graph:
graph{x^23x [5, 7, 4.02, 21.65]}