Which of the following is the equation of the line tangent to the curve $y = \sqrt { x }$ at $x = 9$ ?
(I) y = -x - $\frac { 1 } { 6 }$
(II) y = $\frac { 1 } { 2 }$ x + 3
(III) y = $\frac { 1 } { 6 }$ x + $\frac { 3 } { 2 }$
(IV) y = $\frac { 1 } { 2 }$ $x ^ { - 1 / 2 }$ - $\frac { 1 } { 6 }$
A) IV
B) III
C) I
D) II
E) none of these

Question

Which of the following is the equation of the line tangent to the curve $y = \sqrt { x }$ at $x = 9$ ? 
(I) y = -x - $\frac { 1 } { 6 }$ 
(II) y = $\frac { 1 } { 2 }$ x + 3
(III) y = $\frac { 1 } { 6 }$ x + $\frac { 3 } { 2 }$ 
(IV) y = $\frac { 1 } { 2 }$ $x ^ { - 1 / 2 }$ - $\frac { 1 } { 6 }$
A) IV
B) III
C) I
D) II
E) none of these

Quizplus · Accepted Answer

The derivative of $y = \sqrt { x }$ is $y' = \frac { 1 } { 2 \sqrt { x } }$. At $x = 9$, the slope of the tangent line is $y' = \frac { 1 } { 2 \sqrt { 9 } } = \frac { 1 } { 6 }$. The equation of the tangent line is therefore $y - \sqrt { 9 } = \frac { 1 } { 6 } (x - 9)$, or $y = \frac { 1 } { 6 } x + \frac { 3 } { 2 }$.

Which of the Following Is the Equation of the Line y=xy = \sqrt { x }y=x​

Which of the Following Is the Equation of the Line $y = \sqrt { x }$