Mean Value Theorem II

f ' (c)= f(b)-f(a)/b-a
1. In the graph the slope of point c is parallel to the slope of chord AB which shows that both have the same slope. When solving for f ' (c) you are basically looking for a point in the graph that has the same slope between two points in the graph.

2. In order to meet the conditions of the Mean Value theorem a function needs to be continous and differentiable. In this example the function in the graph is discontinous. The y- axis is an asymptote.The mean value theorem does not apply here because there is no point in the function that has the same slope of points A and B.

3. The function 7sin(x^2) does not satisfy the conditions of the mean value theorem because the graph is continuous but not differentiable. The slope of points A and B is zero but there is no point in the function with a slope of zero. As seen in the graph the peaks are undifferentiable with an undefined slope which means the mean value theorem does not work in this case.

Mean Value Theorem

f ' (c)= f(b)-f(a)/b-a

1. In the graph the slope of point c is parallel to the slope of chord AB which shows that both have the same slope. When solving for f ' (c) you are basically looking for a point in the graph that has the same slope between two points in the graph.

2. In order to meet the conditions of the Mean Value theorem a function needs to be continous and differentiable. In this example the function in the graph is discontinous. The mean value theorem does not apply here because there is no point in the function that has the same slope of points A and B.

In this example the function is continous but not differentiable at x = 3. The function does not satisfy the conditions of the mean value theorem because the slope of points A and B is zero but the slope of point x=3 is undefined. There is no point in the function with a slope of zero.