To find what code the computer generates, we must figure out the points of inflection for the function, which are the points at which the second derivative switches sign. Thus, two points of inflection exist where the second derivative changed in sign. Notice how at the bounds of the intervals, the second derivative is neither positive nor negative.Įvaluating the sign simply by plugging in any value on the given interval into the second derivative function, we find that on the first interval, the second derivative is positive, on the second interval, the second derivative is negative, and on the third interval, the second derivative is positive.
Using the critical value, we now create intervals over which to evaluate the sign of the second derivative: Note that the x values we find are limited by the interval given in the problem statement.
Next, we find the values at which the second derivative of the function is equal to zero: The derivatives were found using the following rules: To determine the points of inflection, we must find the value at which the second derivative of the function changes in sign.
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