Question

Find the equation for the tangent to the curve at a given point.

f(x)= Spuare root (x+5) point (44,7)

Answer 1

\[f(x) = \sqrt {x + 5} \]\[f'(x) = \frac {d}{dx} (x+5)^{1/2} = \frac {1}{2\sqrt {x+5}}\]
\[Y_{tangent} = f'(a)(x-a) + f(a)\]\[f'(44) = \frac {1}{14}, f(44) = 7\]\[Y_{tangent} = \frac {1}{14}(x - 44) + 7\]