Final answer:
To find the curve defined by the equation x³+2xy+y⁴ =13 and sketch it at the point (2,1), substitute the coordinates into the equation and solve for y. Plot the point (2,1) on a graph and determine the shape of the curve.
Step-by-step explanation:
To find the curve defined by the equation x³+2xy+y⁴ =13 and sketch it at the point (2,1), we can first substitute the x and y coordinates into the equation and solve for y.
By substituting x=2 and y=1, we get:
2³ + 2(2)(1) + 1⁴ = 13
8 + 2(2) + 1 = 13
8 + 4 + 1 = 13
13 = 13
Therefore, the equation is satisfied and the point (2,1) lies on the curve defined by the equation.
To sketch the curve, we can plot the point (2,1) on a graph and determine the shape of the curve by plotting additional points or using a calculator or software.