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
The finding of the equations were good, but can you explain what they mean? What does did that equation actually represent?
ReplyDeleteAlso, you need to say why the fact that it is not differentiable makes the Mean Value Theorem not work. Here, you just defined what it meant by not differentiable and showed where it was not differentiable.
Maybe you should develop your ideas a bit more instead of mainly explaining how to find the equations (:
ReplyDeleteYOU should explain more in detail your ideas and maybe placing the graphs next to the explanations would be a helpful
ReplyDelete