Question

Let $f(x)=\frac{x-1}{x^2}$ then which of the following is correct.

• A. $f(x)$ has minima but no maxima.
• B. $f(x)$ increases in the interval $(0,2)$ and decreases in the interval $(-\infty ,0)\cup (2,\infty )$.
• C. $f(x)$ is concave down in $(-\infty ,0)\cup (0,3)$.
• D. $x=3$ is the point of inflection.

Answer 1

Answer: (B), (C), (D)

f^{\prime}(x)=\frac{2-x}{x^3} \text { and } f^{\prime \prime}(x)=\frac{x-3}{x^4} \text {. Now interpret }