Critical number & maximum and minimum values - Derivative Applications

Intro Lesson

• a)

  
  $\bullet$ local maximum
  $\bullet$ local minimum
  $\bullet$ critical number
  

• b)

  
  state the:
  $\bullet$ absolute maximum
  $\bullet$ absolute minimum
  

• c)

  
  on the interval,
  $-1\leq x\leq 12\,$state the:
  $\bullet$ absolute maximum
  $\bullet$ absolute minimum
  

• a)

  
  $f(x)={^3}\sqrt{x^{2}-5x}$

• b)

  
  $f(x)=x^{\frac{1}{3}}-x^{-\frac{2}{3}}$

• a)

  Find the critical numbers.

• b)

  On what intervals is $f$ increasing or decreasing?

• c)

  Find the local maximum and minimum values.

• d)

  Sketch the graph.

• e)

  Find the absolute maximum and minimum values.