Open Question: Please help with Calculus homework on Rolle's Theorem?
Pretty sure f(5) = f(7) in this case. I am not going to do the arithmetic. You can do that.
Rolle's theorem basicly says that if the two end points are equal. There must be a point c between the two end points that have a tangent slope of 0. It's pretty intuitive if you think about it. If the two points have the same y coordinate, than it's either a straight line between them or a curve that goes up then down or etc. There must be a 0 tangent slope somehwere.
To get that point, you set the derivative of f(x) to 0 and solve for x, which is would be the point c.
df/dx = -48 + 8x = 0
x=48/8.... c = 48/8
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