5. Graphical Applications of Derivatives

Which of the following statements best describes the behavior of a function $f$ that satisfies $f\left(0\right)=0$, $f^{\prime }\left(0\right)=3$, $f^{\prime }\left(1\right)=0$, and $f^{\prime }\left(2\right)=-1$?

49–54. {Use of Tech} Graphing with technology Make a complete graph of the following functions. A graphing utility is useful in locating intercepts, local extreme values, and inflection points.

ƒ(x) = 3x⁴ + 4x³ - 12x²

Sketch the graphs of the rational functions in Exercises 53–60.

𝓍²

y = ------------------

𝓍² ― 4