Question

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

Answer 1

derivative?

Answer 2

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

Answer 3

how do i do that with absolute values though?

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

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