Does The Curve Y = 2x3 + 2 Have One Of Its Solutions?

Example 1: Does the curve y = 2x3 – 2 crosses the x-axis between x = 0 and x = 2?

Solution: Solving for the given values of x, at x = 0, then y = 2(0)3 – 2 = -2, the curve is below the x-axis at x = 2, y = 2(2)3 – 2 = 16 – 2 = 14, the curve is above the x-axis,
So the curve crosses the x-axis between x = 0 and x = 2 since y = 2x3 – 2 has a solution found between this interval.

Example 2: From the curve y = x5 - 2x3 – 2, is there a solution between x = 1 and x = 2? Solution: Using the given values of x, At x = 1: y = 15 – 2(1)3 - 2 = -3 At x = 2: y = 25 – 2(2)3 - 2 = 14 Hence, at x = 1, the curve is below zero at x = 2, the curve is above zero

So, somewhere between x = 1 and x = 2 the curve crossed through y = 0. There is a
Between what two values does the equation -5x4 + 6x2 + 1 = 0 have one of its solutions? A. -3 and -2 C. -1 and 0 B. -2 and -1 D. 0 and 1

3. Between what two values does the equation -7x3 + 20x2 - x + 1 = 0 have a solution? A. -1 and 0 C. 1 and 2 B. 0 and 1 D. 2 and 3

4. Between what two values does the equation x3 - 7x - 1 = 0 have a solution? A. -2 and -1 C. 0 and 1 B. -1 and 0 D. 1 and 2

5. Between what two values does the equation -2x3 + 5x − 5 = 0 have a solution? A. -4 and -3 C. -2 and -1 B. -3 and -2 D. -1 and 0

Let us have some cases. (1) A Wobbly Table: [Fix a Wobbly Table (with Math)]
Fixing wobbly table through Intermediate Value