EXAMPLE 1 Find an equation of the tangent line to the function y = 4x2 at the point P(1, 4).

SOLUTION We will be able to find an equation of the tangent line t as soon as we know its slope m. The difficulty is that we know only one point, P, on t, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point Q(x, 4x2) on the graph and computing the slope mPQ of the secant line PQ. We choose x 1 so that P Q. Then

mPQ =
4x2 - 4
x - 1
For instance, for the point Q(1.5, 9) we have

mPQ =

Question

EXAMPLE 1 Find an equation of the tangent line to the function y = 4x2 at the point P(1, 4).

SOLUTION We will be able to find an equation of the tangent line t as soon as we know its slope m. The difficulty is that we know only one point, P, on t, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point Q(x, 4x2) on the graph and computing the slope mPQ of the secant line PQ. We choose x  1 so that P  Q. Then

mPQ =	
4x2 - 4
x - 1
For instance, for the point Q(1.5, 9) we have

mPQ =