Question

Find an equation of the tangent line to the curve at the given point.
y = x³ - 3x + 1, (3, 19)

Answer 1

y=24x-53.

Explanation:

1) the slope-interception view of the required tangent line is

y=slope*x+interception;

2) y'=3x²-3;

3) slope=y'(3), then slope=3*3²-3=24;

4) the required equation of tangent line has the form

y=24x+interception;

5) to calculate the interception it is needed to substitute the given coordinates (3;19) into this equation:

19=24*3+interception; ⇒ interception=-53;

6) finally, the required equation is y=24x-53.