Question

Show that the curve y = 4x - x4 has only 1 stationary point. Determine the nature of this point.

Answer 1

Maximum

Explanation:

dy/dx = 4 - 4x³ = 0

x³ = 1

x = 1

y = 4 - 1 = 3

There's only one stationary point: (1,3)

Nature:

d²y/dx² = -12x²

x = 1, so -12

Negative means it's maximum turning point