Question
A polynomial p(x) has a relative maximum at (-2,4) , a relative minimum at (1,1) , a relative maximum at (5, 7) and no other critical points. How many zeros does p(x) have?
A One
B Two
C Three
D Four
E Five
▶️Answer/Explanation
Ans:B
Question
The function f is continuous on the closed interval [0,2] and has values that are given in the table above. The equation \(f(x)=\frac{1}{2}\) must have at least two solutions in the interval [0,2] if k=
A 0
B \(\frac{1}{2}\)
C 1
D 2
E 3
▶️Answer/Explanation
Ans:A
Question
If a function f is continuous for all x and if f has a relative maximum at (-1, 4) and a relative minimum at (3, -2) , which of the following statements must be true?
A The graph of f has a point of inflection somewhere between x = -1 and x = 3.
B f’(-1) = 0
C The graph of f has a horizontal asymptote.
D The graph of f has a horizontal tangent line at x = 3.
E The graph of f intersects both axes.
▶️Answer/Explanation
Ans:E
Question
Let g be a continuous function on the closed interval [0,1]. Let g(0)=1 and g(1)=0. Which of the following is NOT necessarily true?
A There exists a number h in [0,1] such that \(g(h)\geq g(x)\) for all x in [0,1].
B For all a and b in [0,1], if a=b, then g(a)=g(b)
C There exists a number h in [0,1] such that \(g(h)=\frac{1}{2}\)
D There exists a number h in [0,1] such that \(g(h)=\frac{3}{2}\)
E For all h in the open interval (0,1) , .
▶️Answer/Explanation
Ans:D