calculus
posted by leah .
The slope of the tangent line to the parabola y=4x2–6x+6 at the point where x=5 is:
The equation of this tangent line can be written in the form y=mx+b where m is:
and where b is:

The slope of the tangent at that point will be the same as the slope of the parabola, by definition.
How do you get the slope of the parabola at that point? Differentiate it. What is the differential of 4x^2–6x+6? Now plug in x=5 to your answer, and the arithmetic gives you the slope.
y = mx + b. m is your slope you just got. We need a point on the line to get b.
Where x=5, the point where the line touches the parabola, y=76, so we have the point (5,76).
76=170+b
and that gives you b.