Question

Find an equation of the tangent line to the curve at the given point. y = ln(x2 ? 7x + 1), (7, 0)

Answer 1

Take derivitive
remember chain rule
dy/dx=1/(x² ? 7x+1) times (2x ? 7)
dy/dx=(2x ? 7)/(x² ? 7x+1)
inputting x=7

the slope at x=7 is (14 ? 7)/(49 ? 49+1)=(14 ? 7)/(49 ? 50)
the slope is (14 ? 7)/(49 ? 50)
use point slope form
y-0=(14 ? 7)/(49 ? 50)(x-7)
y=(14 ? 7)/(49 ? 50)(x-7)

I'm going to take a wild guess that the ? means minus because you were able to type a plus sign
in that case, it would be
y=-2(x-7)