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

**Forum_User** · September 30th 2009, 01:24 PM

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?

**pomp** · September 30th 2009, 01:30 PM

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.

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

**skeeter** · September 30th 2009, 01:37 PM

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

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