Question

Find an equation of the tangent line to the curve at the given point. y = x3 − 3x + 2, (3, 20)

Answer 1

Answer:

$y - 20 = 24(x - 3)$

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, has the following format:

$y - y_0 = m(x - x_0)$

In which the point is $(x_0,y_0)$ and the slope is m.

(3, 20)

This means that $x_0 = 3, y_0 = 20$. So

$y - y_0 = m(x - x_0)$

$y - 20 = m(x - 3)$

Slope:

The slope is the derivative of the function at the point:

The function is:

$y = x^3 - 3x + 2$

The derivative is:

$y^{\prime}(x) = 3x^2 - 3$

At the point, we have that $x = 3$. So

$m = y^{\prime}(3) = 3*3^2 - 3 = 27 - 3 = 24$

So the equation to the tangent line to the curve a the point is:

$y - 20 = 24(x - 3)$