NCEA Calculus 2017 TWO(c - Solution & Explanation

Question

The tangent to the curve

y = \sqrt{x}

is drawn at the point

(4,2)

.

Loading diagram...

Find the co-ordinates of the point Q where the tangent intersects the

x

-axis.

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

Official Answer

y=\sqrt{x}

\dfrac{dy}{dx}=\dfrac{1}{2}x^{-\frac{1}{2}}=\dfrac{1}{2\sqrt{x}}

At

(4,2)\ \ \dfrac{dy}{dx}=\dfrac{1}{2\sqrt{4}}=\dfrac{1}{4}

Tangent:

y=\dfrac{1}{4}x+c

through

(4,2)

2=1+c

c=1

y=\dfrac{1}{4}x+1

y=0\ \Rightarrow\ 0=\dfrac{1}{4}x+1

x=-4

Point

Q

is

(-4,0)

.

Grading Criteria

-

-

Video Explanation

NCEA Level 3 Calculus Differentiation 2017 NZQA Exam - Worked Answers by infinityplusone(starts at 28:58)

2017 TWO(c)