Higher Maths Unit Assessment Revision
Applications
1.4 Applications of Calculus
1) Find the values of x which minimises these functions.
a) 𝑓(𝑥) = 𝑥 2 + 50𝑥 + 4
b) 𝑓(𝑥) =
36
𝑥
+ 𝑥,
x>0
1
c) 𝑓(𝑥) = 𝑥 2 + 2𝑥,
x>0
2) Find the value x which maximises these functions.
a) 𝑓(𝑥) = 10 − 2𝑥 − 3𝑥 2
b) 𝑓(𝑥) = 12𝑥 − 𝑥 3 ,
x>0
3) Find the area of the shaded regions in these diagrams.
a)
b)
y = 3x3
y = 9 – x2
–2
4
–3
c)
3
y  x 3  6 x 2  x  30
–2
3
d)
y = x2 – 3x
5
0
y = 3x
6