Is 110 and 112 True or False ### Creating Polynomial FunctionsIn Exercises 103-106, find a polynomial function \[ f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0 \]that has only the specified extrema.#### Instructions:(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.#### Exercises:**103.** Relative minimum: (0, 0); Relative maximum: (2, 2) **104.** Relative minimum: (0, 0); Relative maximum: (4, 1000) **105.** Relative minima: (0, 0), (4, 0); Relative maxima: (2, 4) **106.** Relative minimum: (1, 2); Relative maxima: (-1, 4), (3, 4)### True or False?In Exercises 107-112, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.**107.** There is no function with an infinite number of critical points.**108.** The function \( f(x) = x \) has no extrema on any open interval.**109.** Every \( n \)-th degree polynomial has \( (n - 1) \) critical numbers.**110.** An \( n \)-th degree polynomial has at most \( (n - 1) \) critical numbers.**111.** There is a relative extremum at each critical number.**112.** The relative maxima of the function \( f \) are \( f(1) = 4 \) and \( f(3) = 10 \). Therefore, \( f \) has at least one minimum for some \( x \) in the interval (1, 3).### Graphs/Diagrams Explanation:- **Graph on the Left:** This graph depicts a polynomial

Name: Is 110 and 112 True or False ### Creating Polynomial FunctionsIn Exerc
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Description: Is 110 and 112 True or False ### Creating Polynomial FunctionsIn Exercises 103-106, find a polynomial function \[ f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0 \]that has only the specified extrema.#### Instructions:(a) Determine the