Determine if the following statements are true or false. a. If a function

f

has an absolute maximum on the interval

[1,3]

, then it also has an absolute minimum on the same interval. True

False b. If

f'(4)=0

and

f'(x)<0

for

x<4

, then

f

is changing from decreasing to increasing at

x=4

. False

True c. If a function

f

is continuous on the interval

[0,)

, then it has either an absolute maximum or absolute minimum on the interval. False

True d. On the interval

[1,1]

, the function

f(x)=1x^2/3

satisfies the conditions of Rolle's theorem. True

False e. If

f

is an everywhere continuous and differentiable function where

f'(1)=0

and

f''(1)=0

, then the point corresponding to

x=1

is neither a relative maximum nor relative minimum of

f

. True or Falsa