Question: A straight line intercept the y axis at $x=0$ and and $x$ axis at $y =0$. The line pass through a point $(3,2)$. The line show a negative slope on the graph. A triangle is form under the graph. Is there exist any minimum or maximum area of the triangle form by the line. if yes, state your reason.
Additional detail: I'm a little bit confuse. Am i rite to say that the interception coordinate at $y$-axis is $(0,y)$ and at the $x$ axis is $(x,0)$. So the line pass through 3 point that is $(0,y)$ , $(3,2)$ , and $(x,0)$. Thus, it form a triangle on the graph.
I have seen a video on youtube solving quite a similar question. but the video doesn't show me the way on how to know that the area is minimum or maximum.
Could you please show me how to solve this optimization problem using calculus. Could u show me the right way (step by step) to solve the question. What is the condition for the triangle to have the minimum or maximum area and how to write this in mathematical expression.