# Find the equation of the tangent to the curve

• Mar 18th 2012, 03:08 PM
johnreal
Find the equation of the tangent to the curve
Find the equation of the tangent to the curve y = ln(3x − 2) at the point where x = 1. I differentiated this and got 3/3x-2, whats my next step?
• Mar 18th 2012, 04:12 PM
skeeter
Re: Find the equation of the tangent to the curve
Quote:

Originally Posted by johnreal
Find the equation of the tangent to the curve y = ln(3x − 2) at the point where x = 1. I differentiated this and got 3/3x-2, whats my next step?

to find the equation of a line tangent to a curve defined by \$\displaystyle f(x)\$ at \$\displaystyle x = a\$ ...

1. you need the point of tangency on the curve, \$\displaystyle (a, f(a))\$

2. you need the value of the slope of the curve at the point of tangency , \$\displaystyle m = f'(a)\$

3. now that you have a point \$\displaystyle (a,f(a))\$ and a slope, \$\displaystyle m = f'(a)\$ , write the equation in point-slope form ...

\$\displaystyle y - f(a) = f'(a)(x - a)\$