1.66: Differentiation and a Normal

4PM1/1/January/2019 — Question 6 · 10 marks

Given that

y=x^2\sqrt{2x-3},

(a) show that

\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{x(5x-6)}{\sqrt{2x-3}}.

(4)

(b) Find the value of

\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}

when

\displaystyle x=2

.

(1)

The curve

\displaystyle C

has equation

y=x^2\sqrt{2x-3}.

(c) Find an equation of the normal to

\displaystyle C

at the point on

\displaystyle C

where

\displaystyle x=2

.

Give your answer in the form

\displaystyle ax+by+c=0

, where

\displaystyle a

,

\displaystyle b

and

\displaystyle c

are integers.

(5)