Find all relative extrema and inflection points for the following function. 4) y -2x^3+24x^2+288 x-35

Relative maximum at x=12

Relative minimum at x=-4

Inflection point at x=4

Step-by-step explanation:

To find all the critical points of the function we need the first derivative of the function

According to  Fermat's theorem, it will be a critical point in y'(x)=0, then

With the test of the second derivative, we can know if the points are relative extrema or inflections.

The second derivative test says: if then x is a relative maximum, if then x is a relative minimum. So x=12 is a relative maximum and x=-4 is a relative minimum.

To find the inflection point y''(x)=0

step-by-step explanation:

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step-by-step explanation: