I'm trying to graph the function $f(x,y)=2(x+y)+(x−y)^2−(x+y)^3$ and I'm seeking guidance on how to go about it. Here's what I've done so far:
First, I've defined a range for both $x$ and $y$, specifically, from $-5$ to $5$.
Second, I've calculated the values of the function for various $(x,y)$ pairs within this range.
For example: if $(x,y)=(2,3)$ then:
$f(2,3)=2(2+3)+(2−3)^2−(2+3)^3$
$=2(5)+(−1)^2−(5)^3$
$=10+1−125$
$=−114$
Third, I've created a set of points $(x,y,f(x,y))$ to represent these calculated values:
$(2,3,−114)$
$(1,1,−1)$
$(0,0,0)$
$(−1,−1,−1)$
$(−2,−3,−114)$
Now, I'd like to create a three-dimensional graph with $x$ and $y$ on the $xy$-plane and $f(x,y)$ as the $z$-coordinate. However, I'm not sure how to proceed further or if my approach is correct.
Could someone please provide guidance on how to create this graph?
Thank you in advance for your assistance!