Please do all questions and show work thank you If f is incr

If f is increasing on an interval integration, then f^\'(x) >statement. If integration is increasing and differentiable in I. then f(x) > 0 for all x in i, If cars A and B always have the same speed, then they will always be the same distance apart.

Solution

a)

False

Because f is increasing does not imply f is differentiable.

Counterexample

f=x ,0<=x<=1

f=2x-1, x>=1

ON the interval [0,2] f is increasing but not differentiable at x=1

b)

No.

We can have constant functions because increasing function also includes functions which remain constants ie non decreasing functions

SO, f\'(x)=0 is possible

c)

False.

Cars have the same speed but could have different velocity and could be moving in opposite dirrections and distance then will change with time.