Find an equation of the tangent line to

Question

y=(x^2)-3 at x=2.

Answer 1

Given that y = (x^2)-3

Substituite the value of x = 2 in the given equation

y = (2)^2 - 3

y = 4 - 3 = 1

Slope m = (dy)/(dx)

y = (x^2) - 3

(dy)/(dx) = 2x

(dy)/(dx) = 2(2) = 4

We have points (x1 , y1) = (2 , 1) and slope m = 4

Equation of a tangent line is (y - y1) = m(x - x1)

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

(y - 1) = 4x - 8

Bring all the terms to one side

4x - y - 8 + 1 = 0

4x - y - 7 =0

The required equation of a tangent line is 4x - y - 7 = 0