Transcript The Tangent Line Problem The function f f(c + Δx) f(c) c Δx c + Δx.

The Tangent Line Problem
The function f
f(c + Δx)
f(c)
c
Δx
c + Δx
The Tangent Line Problem
The function f
Secant Line
f(c + Δx)
Connects the two points
(c, f(c)) and (c + Δx, f(c + Δx))
f(c)
c
c + Δx
Problem: Find the slope of the secant line that connects the two
points (c, f(c)) and (c + Δx, f(c + Δx))
y2  y1 f (c  x)  f (c) f (c  x)  f (c)


x2  x1
c  x  c
x
The last term is called a “difference quotient” and it
will prove to be very important in calculus. You must
understand how it was derived.
Secant line to tangent line
Δx
c
Tangent line when Δx “goes to zero”