"How do you find the equation of the..." was answered by our experts

Bryanna Leon

Answered question

2022-04-17

How do you find the equation of the tangent line to the curve

y = x^{3} + 2 x^{2} - 3 x + 2

at the point where x = 1?

Sabrina Campos

Beginner2022-04-18Added 13 answers

To find the equation of the tangent require gradient ( m ) and a
point on the line (a , b ).
The derivative of y

(\frac{d y}{d x}) = m

To find a point on the line use x = 1 substituted into equation
to find y coordinate.

\frac{d y}{d x} = 3 x^{2} + 4 x - 3

when x=1:

\frac{d y}{d x} = 3 {(1)}^{2} + 4 (1) - 3 = 3 + 4 - 3 = 4

and

y = {(1)}^{3} + 2 {(1)}^{2} - 3 (1) + 2 = 1 + 2 - 3 + 2 = 2

equation if tangent is : y - b =m(x - a ) where m = 4 and
( a , b ) = (1 , 2 )
hence

y - 2 = 4 (x - 1) \to y - 2 = 4 x - 4

\Rightarrow y = 4 x - 2

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?