Question

Use this to find the equation of the tangent line to the parabola y = 4x ^ 2 - 4x + 2 at the point (3, 26) . The equation of this tangent line can be written in the form y = mx + b

Answer 1

Let's find the derivative

$\begin{gathered} f^{\prime}(4x^2\text{ -}4x+2)=8x\text{ -}4 \\ f^{\prime}(3)=8(3)\text{ - }4=24\text{ - }4=20 \end{gathered}$

The slope of the tangent line at the point x=3 is 20

$\begin{gathered} y=mx+b \\ 26=20(3)+b \\ b=26\text{ - }60=\text{ -}34 \\ \\ So\text{ }y=20x\text{ -}34 \end{gathered}$