Question

lesson 3 practice problems

1. select all points where

relative minimum values
occur on this graph of a
polynomial function.
a. point a
b. point b
c. point c
d. point d
e. point e
f. point f
g. point g
h. point h

1. add one term to the polynomial expression ( 14x^{19}-9x^{15}+11x^{4}+5x^{2}+3 ) to make

it into a 22nd degree polynomial.

Explanation:

Step1: Recall the definition of relative minimum

A relative minimum is a point where the function changes from decreasing to increasing.

Step2: Analyze each point

• Point \(A\): The function is decreasing before \(A\) (not a relative minimum).
• Point \(B\): The function changes from decreasing to increasing (relative minimum).
• Point \(C\): It is an \(x -\)intercept (not a relative minimum).
• Point \(D\): The function changes from increasing to decreasing (relative maximum).
• Point \(E\): The function changes from decreasing to increasing (relative minimum).
• Point \(F\): The function changes from increasing to decreasing (relative maximum).
• Point \(G\): It is an \(x -\)intercept (not a relative minimum).
• Point \(H\): The function is decreasing (not a relative minimum).

Answer:

B. Point \(B\), E. Point \(E\)