In Exercises find a polynomial function

that has only the specified extrema. 

(a) Determine the
minimum degree of the function and give the criteria you used
in determining the degree. 

(b) Using the fact that the
coordinates of the extrema are solution points of the function,
and that the x-coordinates are critical numbers, determine a
system of linear equations whose solution yields the coefficients
of the required function. 

(c) Use a graphing utility to solve the
system of equations and determine the function. 

(d) Use a
graphing utility to confirm your result graphically.

Relative minimum: (0, 0); Relative maximum: (2, 2)

Transcribed Image Text:

f(x) = a₁x¹ + a₂−1x²−¹ + ・・・ + a₂x² + a₁x + ภ-