Problem: Given a function
f and a specific
x-value
x = c, compute the slope of the
line tangent to
f at
x = c.
We denote this slope by
f ′(c), and we say
f ′(c) is the derivative of
f at
x = c.
Solution:
With the applet above, we'll explore where this formula comes from. Note that
in the applet you can move two points on the
x-axis -- one with
x-value
c, and one with
x-value
c + h.