# tangent lines

• Sep 24th 2007, 09:07 PM
mer1988
tangent lines
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
• Sep 24th 2007, 09:11 PM
Jhevon
Quote:

Originally Posted by mer1988
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