b) use a table of values of f(x)=-x^4 - x^3 + 5x^2 + x - 3 to estimate the x - coordinates at which the…
b) use a table of values of f(x)=-x^4 - x^3 + 5x^2 + x - 3 to estimate the x - coordinates at which the relative maxima and relative minima occur. x f(x) -3 -15 -2 41 -1 1 0 -3 1 1 2 -5 3 -63 the relative maxima occur near x = -2 and x = 1. the relative minimum occurs near x = 0.
Answer
Explanation:
Step1: Analyze the table values
We observe the values of (f(x)) for different (x) - values in the table. When the function changes from increasing to decreasing, a relative maximum occurs. When it changes from decreasing to increasing, a relative minimum occurs.
Step2: Identify relative maxima
As (x) increases from (-3) to (-2), (f(x)) increases from (-15) to (41), and as (x) increases from (-2) to (-1), (f(x)) decreases from (41) to (1). Also, as (x) increases from (0) to (1), (f(x)) increases from (-3) to (1), and as (x) increases from (1) to (2), (f(x)) decreases from (1) to (-5). So relative maxima occur near (x=-2) and (x = 1).
Step3: Identify relative minimum
As (x) increases from (-1) to (0), (f(x)) decreases from (1) to (-3), and as (x) increases from (0) to (1), (f(x)) increases from (-3) to (1). So a relative minimum occurs near (x = 0).
Answer:
The relative maxima occur near (x=-2) and (x = 1). The relative minimum occurs near (x = 0).