Consider the point P= (2,−4) and the function f(x) =x2−6x+ 8. Find the equation(s) of the line(s) passing through point P and tangent to the function f(x).

Answer 1

f(x) =x²−6x+ 8

P= (2,−4), meaning x=2 and y=-4

The derivative of a function is the slope of the tangent line. First, get f'(x).

f'(x)=2x-6, the plug in the value of x:

f'(2)=2(2)-6 = -2.

The slope of a tangent line is -2. We take the point-slope form of linear equation:

y - y₁=m(x - x₁).

Therefore the equation of the line is:

y+4 = -2(x-2)