Tangent Line Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Find the equation of the tangent line to

h(x) = 3x^3 - x

x = 1

1
Point: $h(1) = 3 - 1 = 2$ , so $(1, 2)$ .
2
$h'(x) = 9x^2 - 1$ , so $h'(1) = 8$ . Tangent line: $y - 2 = 8(x - 1)$ , i.e., $y = 8x - 6$ .

Answer

y = 8x - 6

Evaluate the function at the given

x

for the point, differentiate and evaluate for the slope, then use point-slope form.

About Tangent Line

A line that touches a curve at exactly one point and has the same slope as the curve there.

Find the equation of the tangent line to [formula] at [formula].

Find the equation of the tangent line to [formula] at [formula], and use it to approximate [formula]

At what point(s) on [formula] does the tangent line have slope [formula]?