Revision of Mean Value Theorem

1) we all have an idea of what the mean value theorem is and we are doing this entry because of some unclear area in this topic. the mean value theorem finds a point in the given interval that is parallel to two points a and b also in the interval there are certain condition the graph most pass before the mean value theorem can be used and give a definite answer. off the back i do not know the conditions but i believe those conditions are the function must be continuous and differentiable. if it passes that, then the mean value theorem can be used. the equation that i am going to use is √(x) in the interval [0, infinity). REMEMBER the point of the blogs is to show an understanding so I'm going to show u my understanding with this simple Graph. the graph look like this











I'm going to choose x=4, and x=9 for a and b. the out put for x=4 is 2 and for x=9 is 3. simple rite. using the mean value theorem we get a slope of 1/5 . doing the math the point x=25/4 would have an instantaneous slope of 1/5. the tangent line would be y = (x/5)+(5/4) which is going to be represented by the green line. f(a) = 4 and f(b)=9. the secant line witch is not in the graph would have the same slope as the green line y=(x/5)+(5/4).