Chapter 4 - Applications of the Derivative - 4.4 The Shape of a Graph - Exercises - Page 194: 12

concave up $x$ > $0$ concave down $x$ < $0$ inflection point is at $x$ = $0$

let $f(x)$ = $x^{\frac{7}{5}}$ $f'(x)$ = $\frac{7}{5}x^{\frac{2}{5}}$ $f''(x)$ = $\frac{14}{25}x^{-\frac{3}{5}}$ concave up $\frac{14}{25}x^{-\frac{3}{5}}$ > $0$ $x$ > $0$ concave down $\frac{14}{25}x^{-\frac{3}{5}}$ < $0$ $x$ < $0$ inflection point is at $x$ = $0$