# Thread: finding eq. of tan to the slope f(x) given the slope

1. ## finding eq. of tan to the slope f(x) given the slope

I know how to do this problem but I just totally had a brain fade and cant seem to figure it out, can someone lead me into the right direction here?

2. Originally Posted by tecknics
I know how to do this problem but I just totally had a brain fade and cant seem to figure it out, can someone lead me into the right direction here?

$\displaystyle y = \sqrt {x + 9}.$

An equation of the tangent
$\displaystyle \boxed{y = {{y'}_0}\left( {x - {x_0}} \right) + {y_0}}$

$\displaystyle {{y'}_0} = {\left( {\sqrt {{x_0} + 9} } \right)^\prime } = \frac{1} {4} \, \Rightarrow \, \frac{1}{{2\sqrt {{x_0} + 9} }} = \frac{1}{4} \Leftrightarrow \sqrt {{x_0} + 9} = 2 \Rightarrow {x_0} = - 5.$

$\displaystyle {y_0} = \sqrt { - 5 + 9} = \sqrt 4 = 2.$

Finally, you get this equation of the tangent

$\displaystyle y = \frac{1}{4}\left( {x + 5} \right) + 2 = \frac{x}{4} + \frac{{13}}{4}.$

See this picture

3. Perfect! Thank you!