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onegirl
 2 years ago
Find an equation of the tangent line to y = f(x) at x = a. f(x) = sqrt(x^2 + 16), x = 13
onegirl
 2 years ago
Find an equation of the tangent line to y = f(x) at x = a. f(x) = sqrt(x^2 + 16), x = 13

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SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.1\[f(x)=\sqrt{x^2+16}\Rightarrow f(13)=\sqrt{185}\\ f'(x)=\frac{2x}{\sqrt{x^2+16}}\Rightarrow f'(13)=\frac{26}{\sqrt{185}}\] The tangent line is given by the pointslope formula using the point (13, √185) and the slope 26/√185: \[y\sqrt{185}=\frac{26}{\sqrt{185}}(x13)\]

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so thats the equation? @SithAndGiggles

myko
 2 years ago
Best ResponseYou've already chosen the best response.1the derivative is wrong. The nominator should be just x

myko
 2 years ago
Best ResponseYou've already chosen the best response.1rest looks right, just change 26 for 13 and that's it

SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.1Thanks for catching the mistake
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