Answer Check - Find an equation of the tangent line

[ChaoticFlame]

Homework Statement

Find an equation of the tangent line to the curve y = 5x³ at the point

(-3,-135). Enter your equation in y = form.

Homework Equations

The Attempt at a Solution

Taking the derivative of the equation I get

y = 15x², following that I plug in the x value of the given point:
y = 15(-3)²
and get
y = 135

Am I doing this correctly?

 

[quasar987]

First, you should write the derivative of y with a different symbol than "y". Conventional notations for the derivative are y' or dy/dx.

So you have found

y'(x) = 15x² ==> y'(-3)=135,

which is correct. But y'(3) represents the slope of the curve y(x) at the point (-3,-135). You are asked to find an equation for the line of slope 135 and passing through the point (-3,-135).