Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.

Question

f(x) = 7 x - 2 x^2 text( at ) \(-1,-9\)
m =
y =

Answer 1

dy/dx = 7 - 4x
at (-1,-9)
dy/dx = m = 7 - 4(-1) = 11
plug in point
-9 = 11 (-1) + b
-9 = -11 + b
b = 2

Answer 2

For the slope, calculate df/dx at x = -1.

m = df/dx = 7 - 14x = 21

y = 21x + b

-9 = -21 + b
b = 12
y = 21x +12