Assignment #6

The second derivative test is used to determine whether or not at specific x values in a differentiable function can have relative extrema. This is determined by plugging in the critical numbers of the equation, making the equation positive or negative. If it is negative there it is concave down and has a relative max, if it is positive then it is concave up creating a relative min. To do all this you must use the first derivative, which finds the critical numbers allowing you to determine the concavity, relative max and relative min.

Assignment #5

Due to the use of a differentiable function, f(3)=30 and f(5)=30 therefore f(3)=f(5). This also means that there is a different value for x between 3 and 5, which is f(4)=25. According to Rolle's Theorem, there must be at least one point between 3 and 5 where the rate is equal to 0