The mean value theorem is when F(c)=F(b)-F(a)/(b-a)
1) In this graph i can show u y this is true using two points like x=0 and 2
F(2)-F(0)/2-0=4-0/2=the slope 2 on the tanget line
2) Now we use the y1-y2=m(x1-x2) using the F(2)=4 we have (2,4) which we plug in the equation
y-4=2(x-2)=y=2x the equation of the secent line
3) Using that we can find wat C is by pluging c into F(x)= to the average slope 2c=2 which equals c=1 showing that at c=1 they have the same slope
Question #2
This equation is continous but nat differentible because at the x slope of a and b is 0 but thier is no point where x is 0 in this equation
Like the second graph