1.25: The curve with equation has a stationary point with coordinates where and are integers.

4PM1/1R/June/2023 — Question 7 · 8 marks

The curve with equation

\displaystyle y = mx^2 + 64\sqrt{x} + 39

has a stationary point with coordinates

\displaystyle (4, n)

where

\displaystyle m

and

\displaystyle n

are integers.

Using calculus

(a) find the value of

\displaystyle m

and the value of

\displaystyle n

(6)

(b) determine the nature of the stationary point.

(2)