Is 90 and 92 True or False

90)

Given that f(x)=1/x is concave downward for x<0 and concave upward for x>0 and thus it has a point of inflection at x=0.

We need to check whether the given statement is True or False.

Solution:

To find the inflection point we need to find the second derivative of the function and check where the second derivative of the function is zero.

$$\begin{gathered} f\left(x\right)={x^{-}}^1 \\ f\text{'}\left(x\right)=-1x^{-2} \\ f\text{'}\text{'}\left(x\right)-1(-2)x^{-3} \\ f\text{'}\text{'}\left(x\right)=\frac{2}{x^3} \end{gathered}$$

given that the function as inflection at x=0 but at x=0 the second derivative of the function is not defined and no inflection exists for this function.

Hence the given statement is False.