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

  1. #1
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    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?
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    Quote Originally Posted by Forum_User View Post
    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
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  3. #3
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    Quote Originally Posted by Forum_User View Post
    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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