Find the equation of the tangent to the graph at the indicated point.

Question

f(x)=x^2-6x; a=-9

y=?

Answer 1

y = x^2 - 6x

y' = 2x - 6

the slope is M=f'(-9)

= 2(-9)-6

= -18-6

= -24

But f(-9) = (-9)^2 - 6(-9)

= 81 + 54

= 135

so the tangent line has slope -24 and eats (-9,135)

B = y - mx

= 135 - (-24)(-9)

= 135 - (216)

= -81

y = -24x - 81

Answer 2