A,C,D are true.
The Intermediate Value theorem says that there is a zero in (-2,1) and (1,4)
Rolle's Theorem (or MVT) says that f'(x)=0 somewhere in (-2,4)
Mean Value Theorem says D is true
The function f is continuous on the closed interval [-5,5], and f(-2) = 6, f(1) = -3, and f(4) = 6. Which of the following statements must be true?
A. The equation f(x) = 0 has at least two solutions on the closed interval [-5,5].
B. The equation f(x) = 0 has exactly two solutions on the closed interval [-5,5]
C. The equation f'(x) = 0 has at least one solution on the closed interval [-5,5].
D. The equation f'(x) = 3 has at least one solution on the open interval (1,4).
E. The graph of f has at least one point of inflection on the closed interval [-5,5].
I can't choose between A and C. The graph of f(x) changes between positive and negative twice, so A might be the answer. But that also means it has a positive and negative slope, so C also seems correct.
1 answer
1 answer