Question

for the function f(x)=x^3-3x^2+2 find the interval(s) on which increasing, decreasing, concave up & down, minima (if any), maxima (if any), inflection points (if any)

Answer 1

If you take a derivative of the equation and set it = to 0 and then find the x's you will get your critical points. Then you can use the x variables to plug back in for the y coordinate by using a table of x values. You can check for max and mins by looking at the y coordinate list if given a specific interval, the highest value of y would be your max and the lowest value would be your min. But if no specific interval is given you can graph the derivative you can just look at the highest exponent of the original equation. If it has an odd power (which this one does) there won't be any max/mins because the graph is going towards negative/positive infinity.

Answer 2

ignore (you can graph the derivative)

Answer 3

For concavity you have to take 2 derivatives of the 1st equation and set that equation to 0 also. Then solve for x. You may choose to graph this 2nd derivative, once you graph it whatever portion of the graph is below the x intercept, it will be concave down and whatever portion of the graph is above the x intercept, it will be concave down. Hope this helps.

Answer 4

above x intercept is concave up i mean*