Question

how to find the equation of a line perpendicular to Y=3x^2-4

Answer 1

It will change depending on the point to which you want it to be perpendicular.

Answer 2

Suppose you want it to be perpendicular at \((x_0,y(x_0))\)

Answer 3

oh yeah, at the point (2,1)
sorry

Answer 4

Find the instantaneous with the derivative. To make it perpendicular, you invert it and multiply it by negative one.

Answer 5

So the slope is: \[
m = -\frac{1}{y'(2)}
\]

Answer 6

Using slope point formula: \[
(y-y_0) = m(x-x_0)
\]In this case we have: \[
y-1 = \frac{1}{f'(2)}(x-2)
\]

Answer 7

I changed to \(f\) because in this case \(y\) is the perpendicular line, while I want \(f\) to represent our original curve.

Answer 8

Perfect. Thank you!