Question

find the inflection point for the function shown below. if there are more than one, be sure to spearate them by using a comma. if there is not an inflection point, record dne in the answer box.

$f(x)=\frac{3}{2}x^{2}-39x - 4$

Explanation:

Step1: Find the first - derivative

Using the power rule $\frac{d}{dx}(ax^n)=nax^{n - 1}$, for $f(x)=\frac{3}{2}x^{2}-39x - 4$, we have $f'(x)=3x-39$.

Step2: Find the second - derivative

Differentiating $f'(x)=3x - 39$ with respect to $x$ using the power rule again, we get $f''(x)=3$.

Step3: Set the second - derivative equal to zero

We set $f''(x) = 0$. But $3
eq0$, so there are no solutions for $x$ from the equation $f''(x)=0$.

Answer:

DNE