### Home > CALC > Chapter 8 > Lesson 8.3.3 > Problem8-129

8-129.

Multiple Choice: Given $f(x) =\frac { 1 } { x }−4x^2 + 7x$, then $f$ is concave up for …

1. $x ≠ 0$

1. no values of $x$

1. $x < 0$

1. $x < 0$ or $x >\frac { 1 } { \sqrt [ 3 ] { 4 } }$

1. $0 < x <\frac { 1 } { \sqrt [ 3 ] { 4 } }$

Recall that candidates for points of inflection occur where the 2nd-derivative equals zero AND where the 2nd-derivative does not exist.

After you identify where $f^{\prime\prime}(x) =0$ and where $f^{\prime\prime}(x) =$ DNE, check the regions before, after and between those candidates: if $f^{\prime\prime}(x) > 0$, then $f(x)$ is concave up.