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

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )