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# Intermediate Value Theorem Exercises

### Example 1

• Can we use the IVT to conclude that f(x) = x3 + 2x + 1 passes through y = 0 on the interval (-2, 2)?

### Example 2

• Can we use the IVT to conclude that f(x) = ex passes through y = 0.1 on the interval (0, 1)?

### Example 3

• Can we use the IVT to conclude that f(x) = sin(x) equals 0.4 at some place in the interval ?

### Example 4

• Can we use the IVT to conclude that f(x) = tan(x) equals 0 for some c in (0, π)?

### Example 5

• Can we use the IVT to conclude that f(x) = x2 passes through 1 on the interval (-1, 1)?

### Example 6

• Draw a function that is continuous on [0, 1] with f(0) = 0,  f(1) = 1, and f(0.5) = 20.

### Example 7

• Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous on that interval?