Describing the Behaviour of Functions

f(x) is…

  1. increasing at … if f’(x) > 0
  2. decreasing at … if f’(x) < 0
  3. stationary at … if f’(x) = 0

Example

{}𝑓(𝑥)=𝑥3+4𝑥23

𝑓(𝑥)=𝑥3+4𝑥23𝑓(𝑥)=3𝑥2+8𝑥(𝑓(𝑥)=0)3𝑥2+8𝑥=0𝑥(3𝑥+8)=0𝑥=0or83
𝑓(𝑥)>0𝑥<83or𝑥>0
𝑓(𝑥)<083<𝑥<0