Example
EXAMPLE 1 Find an equation of the tangent line to the parabola
y = 4x^2 at the point P(1, 4) using this definition.
SOLUTION Here we have a = 1, and f(x) = 4x^2, so the slope is
$\lim_{x \to 1} \frac{f(x) - f(1)}{x - 1}$
= $\lim_{x \to 1} \frac{\text{ }}{x - 1}$
= $\lim_{x \to 1} \frac{4(x - 1)(\text{ })}{x - 1}$
= $\lim_{x \to 1} 4(\text{ })$
= + 4 =
Using the point slope form of the equation of a line, we find an equation
of the tangent line at (1, 4) is
y - = (x - ) or y = x -
