Evaluate
WOLFRAM|DEMONSTRATIONS PROJECT

Secant and Tangent Lines

​
x
0
h
tangent line
-1.0
-0.5
0.5
1.0
x
-80
-60
-40
-20
20
40
y
f(x) = -x
3
+x
2
+12x-3
​
secant slope = -{BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>]}[-4] + {BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>], BooleanFunction[<2>],
BooleanFunction[<2>], BooleanFunction[<2>]}[-3]

This Demonstration illustrates the connection between the secant line and the tangent line at a point on a curve. You can vary the point of tangency and the difference
h
of the
x
values of the two points defining the secant line.