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

1. ## 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 $\displaystyle f(x)=\sqrt{x+3}$ at the point $\displaystyle P(4,5)$

Can anyone provide hints on how to solve this?

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

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.

$\displaystyle f(4) = \sqrt{4+3} = \sqrt{7} \neq 5$

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

Can anyone provide hints on how to solve this?
slope = $\displaystyle f'(4) = \lim_{x\to 4} \frac{f(x) - f(4)}{x-4}$