Interactive-12Adv-Concavity & points of inflection

$$x<\frac{1}{6}$$

$$x<-1/6$$

$$x>-1/6$$

$$x>\frac{1}{6}$$

$$(-∞,\frac{1}{6})$$

$$\left(\frac{7}{3},∞\right)$$

$$(-∞,-\frac{1}{6})$$

$$\left(-\frac{7}{3},∞\right)$$

The first derivative is zero.

The second derivative is greater than zero.

The second derivative is zero and the concavity changes.

The second derivative is less than zero.

f''(x) = 0 and f'(x) > 0

f''(x) = 0 and f'(x) = 0

f''(x) > 0 and f'(x) = 0

f''(x) < 0 and f'(x) = 0

$$x=0,x=1$$

$$x=-1,x=1$$

$$x=0,x=-1,x=1$$

$$x=0,x=-1$$

The first derivative is zero and the second derivative changes sign.

The second derivative is zero and the second derivative changes sign.

The first derivative is zero and the second derivative does not change sign.

The second derivative is zero and the second derivative does not change sign.