# Question: come up with your own twicedifferentiable function and draw its...

###### Question details

Come up with your own twice-differentiable function and draw its graph without a calculator by analyzing its properties. These properties must be included: zeros, symmetry, and first- and second-order derivatives, local and global extreme values, the concavity test, concave up, and concave down. Then, graph your function using your graphing calculators to verify your work.

Here is some additional guidance:

define your function:

don’t make your function too complex or too simple

do not use f(x)=x^2 or something real lame

you are free to incorporate trig functions

factor your function to locate the zeros

describe symmetry with respect to x-axis, y-axis, and origin

Find first derivative and second derivative

Use the first and/or Second Derivative tests to identify local and/or absolute extreme values

Using the second derivatives, describe intervals where the function is concave up and concave down

include a graph of your function

can be hand drawn or done using Desmos

I promise to upvote your response!! :) Thanks!