Question

Consider the parabola y = 6x − x2.
(a) Find the slope of the tangent line to the parabola at the point (1, 5).

(b) Find an equation of the tangent line in part (a).

Answer 1

((6(1+h) - (1+h)^2 ) -(6(1)-1^2) / h
6+6h -(1+2h +h^2) - 6 +1 / h
6 + 6h - 1 -2h - h^2 - 6 + 1 /h

4h - h^2 /h
4-h
h ->0
so slope is 4

Answer 2

y = mx + b
5 = 4(1) + b
1 = b
y = 4x + 1