Let h(12) = -100 for some function h(x), defined everywhere. If the average rate of change of h(x) from x = 12 to x = 20 is 50, then find h(20).
To find h(20), we can use the average rate of change formula. The average rate of change of a function from x = a to x = b is given by:
Average rate of change = (f(b) - f(a)) / (b - a)
In this case, we have the average rate of change as 50, x = 12, and x = 20. We also know that h(12) = -100.
Using the formula, we can substitute the given values:
50 = (h(20) - (-100)) / (20 - 12)
Simplifying the equation:
50 = (h(20) + 100) / 8
Cross-multiplying:
8 * 50 = h(20) + 100
400 = h(20) + 100
Subtracting 100 from both sides:
400 - 100 = h(20)
300 = h(20)
Therefore, h(20) is equal to 300.