MEANIE

The mean value theorum means: F'(c) is the derivative at x=c and the slope of the secant line through the interval [a,b] is F(b)-F(a)/b-a all this basically means this Point of Secant line is equal to the Point of the Tangent line.
For Instance my graph would be x²


lets say the intervals are from [o,3] so then a=0 and b=3 now we got the points now all we need is to use them in the equation and find c so F(3)-F(0)/3-0 =3 so the slope of the secant line is 3 and the equation is the derivative 2x



Ok so skipping all of the equations blah blah blah we find that c lies on x=1 and knowing that we can do the tangent line. Which again blah blah blah we find that it passes through (1,1)and since the tangent line is parallel to the secant use that knowledge and pont slope form and then we get the equation F(x)=2x-1 and bam definition graphically



2. this doesnt work for equations that end up being cusps, corners, etc like and absolute value equation it is not diferrentible at x=0 so there is no tangent point there right? hehehe