Is #f(x)=x^2-3x # 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^2-3x#

#f'(x)=2x-3#

Find the sign of the derivative at #x=-2#.

#f'(-2)=2(-2)-3=-7#

Since #f'(-2)<0#, the function is decreasing at #x=-2#.

We can check by consulting a graph:

graph{x^2-3x [-5, 7, -4.02, 21.65]}