tangent lines

**mer1988** · September 24th 2007, 09:07 PM

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

**Jhevon** · September 24th 2007, 09:11 PM

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 $y = mx + b$ where $m$ is the slope, and $b$ is the y-intercept.

how do we find the slope? well, from the derivative of course. find $y'$ and plug in $x = 3$ to get the slope at that point, then use the point slope form.

$y = y_1 = m(x - x_1)$

where $(x_1,y_1)$ is the point on the graph when $x = 3$

just solve for y to get the equation of the line

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