Find the equation of the tangent line to the curve when $x$ has the given value.
-$f(x)=\sqrt{x} ; x=4$
A) $y=\frac{x}{4}+1$
B) $y=-7 x+28$
C) $y=-7 x-9$
D) $y=\frac{x}{2}-\frac{1}{2}$

Question

Quizplus · Accepted Answer

The derivative of $f(x)=\sqrt{x}$ is $f'(x)=\frac{1}{2\sqrt{x}}$. At $x=4$, $f'(4)=\frac{1}{4}$. The point on the curve is $(4,2)$. The equation of the tangent line is $y-2=\frac{1}{4}(x-4)$, which simplifies to $y=\frac{x}{4}+1$.

Find the Equation of the Tangent Line to the Curve xxx

Find the Equation of the Tangent Line to the Curve $x$