Calc Review 12/7

Does  $f\left(x\right)=2+x-x^2$  holds with IVT given  $\left[0,3\right];\ w=1$  ?

• IVT holds

• IVT does not hold

• no sufficient information

Let f be a continuous function for which f(-2)=1 and f(5)=-3. The Intermediate Value Theorem guarantees that

• f(c)=2 for at least one c between -3 and 1

• f(c)=0 for at least one c between -2 and 5

• f(c)=0 for at least one c between -3 and 1

• f(c)=2 for at least one c between -2 and 5

Given the function  $f\left(x\right)=x^3+x-3$  which of the intervals below contains a zero?

• [-1,1]

• [0,1]

• [1,2]

• None of these intervals

Let f be a function that is continuous on the interval [1, 10]. If f(2) = -5 , f(5) = 5 and f(9) = -5, which must be true?

I. f(x) has a least 2 zeros

II. For some c, 2 < c < 9, f(c) = 3

III. The graph of f(x) has a horizontal tangent

• I only

• I and II

• I, II, and III

• II and III

Find the value that makes the function continuous

• c=1/3
• c=3
• c=-3
• c=-1/3