Find the point of inflection of the graph of the function on the interval .

Question

Find the point of inflection of the graph of the function  on the interval  .

Quizplus · Accepted Answer

The point of inflection occurs where the second derivative changes sign. 
Taking the first derivative of 11eaa595_65ba_2770_a696_75fbd898e983_TB4584_11_TB4584_11, we get:
44x^3 - 36x^2 - 24x + 15
Taking the second derivative, we get:
132x^2 - 72x - 24
Setting this equal to zero and solving for x, we get:
x = (6 + sqrt(63))/22 or x = (6 - sqrt(63))/22
Plugging these values into the second derivative, we see that it changes sign at x = (6 + sqrt(63))/22, which is approximately 0.808. Therefore, the point of inflection is at approximately (0.808, 11eaa595_65ba_7595_a696_f1d43ea34397_TB4584_11_TB4584_11).

Find the Point of Inflection of the Graph of the Function