CAIE IGCSE Additional Math 14.8 Apply Differentiation to Maxima and Minima Questions

Correct use of $x^{2} h=5$ to find an expression that
can be used to eliminate h
M1 for $x^{2} h=5$ soi

Surface area: $x^{2}+4 x\left(\frac{5}{x^{2}}\right)$ oe
Derivative of the surface area: $2 x-20 x^{-2}$ oe
FT their surface area of form $a x^{2}+\frac{b}{x}$

Equates their $2 x-20 x^{-2}$ to 0 and solves to find
a value of x
FT their derivative of form $a x+\frac{b}{x^{2}}$ oe

x=2.15 or $2.154[\ldots] h=1.08$ or $1.077[\ldots]$ nfww
x=2.15 or $2.154[\ldots]$
h=1.08 or $1.077[\ldots]$ nfww
dep on all previous marks awarded

Alternative

Correct use of $x^{2} h=5$ to find an expression that
can be used to eliminate x
M1 for $x^{2} h=5$ soi

Surface area: $\left(\sqrt{\frac{5}{h}}\right)^{2}+4 h \times \sqrt{\frac{5}{h}}$ oe
Derivative of the surface area: $4 \sqrt{5} \times \frac{1}{2} h^{-\frac{1}{2}}-\frac{5}{h^{2}}$
oe
FT their surface area of form $\frac{a}{h}+b \sqrt{h}$

Equates their $4 \sqrt{5} \times \frac{1}{2} h^{-\frac{1}{2}}-\frac{5}{h^{2}}$ to 0 and solves
to find a value of h
FT their derivative of form $\frac{a}{\sqrt{h}}+\frac{b}{h^{2}}$ oe

h=1.08 or $1.077[\ldots] x=2.15$ or $2.154[\ldots]$ nfww
h=1.08 or $1.077[\ldots]$
x=2.15 or $2.154[\ldots]$ nfww
dep on all previous marks awarded