Question

How do I find the equation of the tangent line to the curve at the given point, (2, -4)? y=4x-3x^2.

Answer 1

Equation of tangent line is `y= -8x+12`

Explanation:

Point `(2,-4)` , Curve: `y=4x-3x^2 :.` Slope of the curve

`y'= 4-6x :.` Slope of the curve at point `(2,-4)` is

`m=y'=(4-6*2)=-8`. Equation of tangent line in slope

point form at point `(2,-4)` is `y+4= -8(x-2)` or

`y= -8x+12` [Ans]