Question

F(x)=x³+4x²-5x-4; a=9, b=-1 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. By the intermediate value theorem, the function does not have at least one real zero between a and b because f(a)= (Simplify your answers.)

B. By the intermediate value theorem, the function has at least one real zero between a and b because f(a)=

C. It is impossible to use the intermediate value theorem in this case.

Answer 1

The function has at least one real zero between a = 9 and b = -1

Step-by-step explanation:

The question asks about the function f(x) = x³ + 4x² - 5x - 4 and its real zeros between a = 9 and b = -1. To determine if there is at least one real zero between a and b, we can use the intermediate value theorem. First, evaluate f(a) and f(b). For a = 9, f(a) = 9³ + 4(9)² - 5(9) - 4 = 775. For b = -1, f(b) = (-1)³ + 4(-1)² - 5(-1) - 4 = -3.

Since f(a) = 775 and f(b) = -3 have opposite signs, we can conclude that by the intermediate value theorem, the function f(x) has at least one real zero between a = 9 and b = -1.