how do you find the slope of the curve at the indicated point?
(problem attached)

Question

how do you find the slope of the curve at the indicated point? 
(problem attached)

anonymous · Answer

derivative?

anonymous · Answer

$$f(x)= \left| x \right| $$ at A)x=2 and B)x=-3

anonymous · Answer

how do i do that with absolute values though?

anonymous · Answer

you can treat the absolute values as 2 seperate equations
f(x)=x when x>0
f(x)=-x when x<0

anonymous · Answer

so for problem a
x=2

since 2 is greater than 0, we use f(x)=x

find the derivative, then plug in for x

anonymous · Answer

the graph of x is a straight line with 45° of inclination (slope=1) and its absolute value trows every part of the line that is below the x axis to the its oposite in the upper part of the graph, and since the slope is the opposite to the original line it is -1.|dw:1347937123296:dw|

anonymous · Answer

So the slope for x>0 is 1 and for x<0 is -1