NCEA Calculus 2022 ONE(c - Solution & Explanation

Question

The graph below shows the function

y = \sqrt{x + 2}

, and the normal to the function at the point where
the function intersects the

y

-axis.

Loading diagram...

Find the coordinates of point P, the

x

-intercept of the normal.

*You must use calculus and show any derivatives that you need to find when solving this problem.*

Official Answer

y=\sqrt{x+2}

\dfrac{dy}{dx}=\dfrac{1}{2}(x+2)^{-\frac{1}{2}}

=\dfrac{1}{2\sqrt{x+2}}

At

x=0

,

\dfrac{dy}{dx}=\dfrac{1}{2\sqrt{2}}

and

y=\sqrt{2}

Equation of normal is

y=-2\sqrt{2}x+\sqrt{2}

x

intercept

(y=0)

0=-2\sqrt{2}x+\sqrt{2}

x=\dfrac{1}{2}

Coordinate of

P

is

\left(\dfrac{1}{2},0\right)

Grading Criteria

-

-

Video Explanation

2022 NCEA L3 Calculus Exam Walkthrough by infinityplusone(starts at 4:45)

2022 ONE(c)