Find an equation of the tangent line to the graph of the function $f ( x ) = 2 \sqrt { x }$ at the point that has x-coordinate $x = 36$ . [Hint: use point-slope formula to find the equation of the tangent line.]
A) $y = - \frac { x } { 6 } - 6$
B) $y = \frac { x } { 6 } + 6$
C) $y = 6 x + 6$
D) $y = 6 x + \frac { 1 } { 6 }$
E) $y = \frac { x } { 36 } + 6$

Question

Find an equation of the tangent line to the graph of the function $f ( x ) = 2 \sqrt { x }$ at the point that has x-coordinate $x = 36$ . [Hint: use point-slope formula to find the equation of the tangent line.]  
A)  $y = - \frac { x } { 6 } - 6$
B) $y = \frac { x } { 6 } + 6$
C) $y = 6 x + 6$
D) $y = 6 x + \frac { 1 } { 6 }$
E) $y = \frac { x } { 36 } + 6$

Quizplus · Accepted Answer

First, find the derivative of $f(x) = 2\sqrt{x}$ to get $f'(x) = \frac{1}{\sqrt{x}}$. At $x = 36$, $f'(36) = \frac{1}{6}$, and $f(36) = 12$. Using the point-slope formula with the point (36, 12) and slope $\frac{1}{6}$, the equation is $y - 12 = \frac{1}{6}(x - 36)$, simplifying to $y = \frac{x}{6} + 6$.

Find an Equation of the Tangent Line to the Graph f(x)=2xf ( x ) = 2 \sqrt { x }f(x)=2x​

Find an Equation of the Tangent Line to the Graph $f ( x ) = 2 \sqrt { x }$