Answer to Question #265354 in Calculus for Wanie

Question

the equation of a curve is given as f(x)= sqrt 2x-1, find the equation of the tangent line to the graph of f(x) at x=5

Answer 1

$y=\sqrt{2x-1}$

$y(5)=\sqrt{10-1}=3$

$y'=\frac{1}{\sqrt{2x-1}}$

$y'(5)=\frac{1}{\sqrt{10-1}}=\frac{1}{3}$

Tangent line: $y-3=\frac{1}{3}(x-5)$ or $y=\frac{1}{3}x+\frac{4}{3}$