You are given a continuous polynomial function f(x) with select values shown in the table. x f(x) 0 −9 1 4 2 23 3 −1 4 2 What is the minimum number of values of x where f(x)=0 ? (1 point) Responses 2 2 0 0 1 1 3 3 4 4 Question 2 Part B For the same continuous polynomial function f(x) with select derivative values shown in the table, what is the minimum number of values of x where the slope of f(x) is zero? x f′(x) 0 −4 1 1 2 −5 3 3 4 7 (1 point) Responses 0 0 1 1 2 2 3 3 4 4 Skip to navigation
To find the minimum number of values of x where f(x) = 0, we look for the x-values in the table where f(x) is equal to zero. From the given values, we can see that f(1) = 4, f(3) = -1, and f(4) = 2. Therefore, there are no values of x in the given table where f(x) is equal to zero.
For the second question, we are given the values of the derivative f'(x) at various x-values. To find the minimum number of values of x where the slope of f(x) is zero, we look for the x-values in the table where f'(x) is equal to zero. From the given values, we can see that f'(0) = -4, f'(1) = 1, f'(2) = -5, f'(3) = 3, and f'(4) = 7. Therefore, there is only one x-value (x = 1) where the slope of f(x) is zero.