Graph the following function on its domain. The first and second derivative are given. f ( x ) = x 4 16 − x 3 12 − x 2 + 3 x + 2 f\left(x\right)=\frac{x^4}{16}-\frac{x^3}{12}-x^2+3x+2 f ′ ( x ) = 1 4 ( x − 2 ) 2 ( x + 3 ) f^{\prime}\left(x\right)=\frac14\left(x-2\right)^2\left(x+3\right) f ′ ′ ( x ) = 1 4 ( x − 2 ) ( 3 x + 4 ) f^{\prime\prime}\left(x\right)=\frac14\left(x-2\right)\left(3x+4\right)

Table of contents

5. Graphical Applications of Derivatives

Curve Sketching

5. Graphical Applications of Derivatives

Curve Sketching: Study with Video Lessons, Practice Problems & Examples

27PRACTICE PROBLEM

ANSWERS OPTIONS

Graph of a polynomial function with a red curve, showing its behavior across the x-axis from -7 to 5 and y-axis from -10 to 10.

Graph of the function f(x) = (x^4/16) - (x^3/12) - x^2 + 3x + 2, showing its curve on a Cartesian plane.

Graph of a polynomial function with a red curve, showing its behavior across the x and y axes on a grid.