The blue line would be the tangent line (derivative) and the green line would be the secant line.by using the mean value theorem, we can prove that the tangent and secant line are parallel to one another.
If we use the interval [0,2], then the equation of the tangent line is 2x-1.
The derivative would be 2x.
They would be parallel at x=1.
The mean value theorem fails when:
There is a point when the function is not differentiable.
such as: f(x)=abs(x)
And where a function would be discontinuousan example would be at f(x)=1/x
The function would be discontinuous at x=0.
"the slope of the tangent line and the slope of the secant line are parallel to each other"
ReplyDeleteWhat secant line and what tangent line are you talking about? Any tangent line and any secant line?
"If we use the interval [0,2], then the equation of the tangent line is 2x-1.
The derivative would be 2x.
They would be parallel at x=1."
How did you get these? Why suddenly the derivative in the middle? What would be parallel at x=1?
Also, those are correct examples of discontinuous and non differentiable functions, but WHY do they fail the Mean Value Theorem?
your graphs are good, but a better explanation is better! :0
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