hey i need some help with tangent lines, i just dont understand it at all. I need to figure out how to find the equation of the tangent line to f(x)=x^3 at the point where x=3...much thanks
remember, a line is of the form $\displaystyle y = mx + b$ where $\displaystyle m$ is the slope, and $\displaystyle b$ is the y-intercept.
how do we find the slope? well, from the derivative of course. find $\displaystyle y'$ and plug in $\displaystyle x = 3$ to get the slope at that point, then use the point slope form.
$\displaystyle y = y_1 = m(x - x_1)$
where $\displaystyle (x_1,y_1)$ is the point on the graph when $\displaystyle x = 3$
just solve for y to get the equation of the line