## Calculus, 10th Edition (Anton)

$f’(x) = 3x^2$ The equation of the tangent line: $y = 0$
$f(x) = x^3$ Find the derivative: $f’(x) = \lim\limits_{ Δx\to 0} \frac{f(x+Δx) - f(x)}{Δx}$ $f’(x) = \lim\limits_{ Δx\to 0} \frac{(x+Δx)^3 - x^3}{Δx}$ $f’(x) = \lim\limits_{ Δx\to 0} \frac{x^3 +3x^2Δx+3x(Δx)^2 + (Δx)^3-x^3}{Δx}$ $f’(x) = \lim\limits_{ Δx\to 0} \frac{ Δx(3x^2+3xΔx + (Δx)^2)}{Δx}$ $f’(x) = \lim\limits_{ Δx\to 0} (3x^2+3xΔx + (Δx)^2)$ $f’(x) = 3x^2+3x(0) + 0^2$ $f’(x) = 3x^2$ When x = a, $f(0) = 0$ and $f’(0) = 0$ Find the equation for the tangent line: $(y - y_1) = m(x-x_1)$ $(y - 0)=0(x-0)$ $y_{tangent} =0$ $f’(x) = 3x^2$ The equation of the tangent line: $y = 0$