Let f R rightarrow R2 be defined by ft 2 t2 2t3 a The level

Let f: R rightarrow R^2 be defined by f(t) = (2 t^2, 2t^3). (a) The level sets of f are all subsets of R^k for k = 1 (b) Find all points in the level set of f at level (50, 250). If there is more than one point, enter your answers as a comma separated list.

Solution

here we need to find level surface at apoint (50,250)

By definition level surface at (x₀,y₀) are points on f for which f at those points is (x₀,y₀)

here (x₀,y₀) =(50,250)

So we need to have _2t²=50 and 2t³=250 by definition of f so t² =25 so t= 5 or -5

llly, t³= 125 so t=5

so (5,5),(-5,5) are only two points at level of (50, 250)