IVT, EVT, MVT

• IVT

• EVT

• MVT

• IVT

• EVT

• MVT

• IVT

• EVT

• MVT

• IVT

• EVT

• MVT

The Mean Value Theorem can be applied to which of the following functions on the closed interval [-5, 5]?

•  $f\left(x\right)=\frac{1}{\sin x}$  

•  $f\left(x\right)=\frac{x-1}{\left|x-1\right|}$  

•  $f\left(x\right)=\frac{x^2}{x^2-36}$  

•  $f\left(x\right)=\frac{x^2}{x^2-4}$  

Selected values of the differentiable function f are given in the table above. What are the few possible numbers of c in the interval [1,9] for which the Mean Value Theorem guarantees

 $f'\left(c\right)=6$  ?

• 0

• 1

• 2

• 3

• f has a relative minimum at x = -1

• f has a relative maximum at x = -1

• f has neither a relative minimum nor a relative maximum at
    $x=-1$  

• There is insufficient information to determine whether f has a relative minimum, a relative maximum, or neither at $x=-1$