Question

The slope of the the tangent line to a curve at a point. Calc derivative help

Answer 1

y = 108x + 216

Explanation:

given

y = 4x³ then
`(dy)/(dx)` = 12x² =
`m_(tgt)`

x = 3 ⇒ m = 12(- 3)² = 108

equation of tangent in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept ), hence

y = 108x + b

To find b substitute (- 3, - 108) into the equation

- 108 = -324 + b ⇒ b = - 108 + 324 = 216

y = 108x + 216 ← equation of tangent