Question

Let f(x) = x*(2-x) if x>=0, or x*(x+2) if x<0

i) graph the function from x=-3 to x=+3. If you like WolframAlpha, use Piecewise[{{x*(2-x),x=>0},{x*(x+2),x<0}}]

If you like Desmos, use f(x)= {x>=0:x*(2-x), x<0:x*(x+2)}

(for some reason, when you paste that it, it forgets the first curly-brace { so you’ll need to add it in by hand) Or, you can use this, but it makes it less clear how to take the derivative:

f(x) = -sign(x)*x*(x - 2*sign(x) )

ii) Find and graph its derivative, by hand. You might need to do some algebra before taking the derivative. Notice that you should take the derivative of the formula for when x<0 separately from the derivative for when x>0, but then graph it all on one graph.

iii) Find and graph its 2nd derivative

Answer 1