# New to Calc, need help with "Slope of the line tangent to the function at a point"

• Sep 30th 2009, 02:24 PM
Forum_User
New to Calc, need help with "Slope of the line tangent to the function at a point"
Question:
Find the slope of the line tangent to the function $f(x)=\sqrt{x+3}$ at the point $P(4,5)$

Can anyone provide hints on how to solve this?
• Sep 30th 2009, 02:30 PM
pomp
Quote:

Originally Posted by Forum_User
Question:
Find the slope of the line tangent to the function $f(x)=\sqrt{x+3}$ at the point $P(4,5)$

Can anyone provide hints on how to solve this?

HINT: At P (4,5), f and it's tangent at this point have the same slope/gradient.

EDIT: Hold on, the point (4,5) isn't even on the curve for f.

$f(4) = \sqrt{4+3} = \sqrt{7} \neq 5$
• Sep 30th 2009, 02:37 PM
skeeter
Quote:

Originally Posted by Forum_User
Question:
Find the slope of the line tangent to the function $f(x)=\sqrt{x+3}$ at the point $P(4,5)$

Can anyone provide hints on how to solve this?

slope = $f'(4) = \lim_{x\to 4} \frac{f(x) - f(4)}{x-4}$