Answer:
Explanation:
To apply the intermediate value theorem, we need to show that the function f(x) = x^2 + 3x + 2 is continuous on the closed interval [0, 5].
Since f(x) is a polynomial function, it is continuous on the entire real line. Therefore, it is also continuous on the closed interval [0, 5].
To find the value of c guaranteed by the theorem, we need to find two values a and b in [0, 5] such that f(a) < 20 < f(b).
We have:
f(0) = 2
f(5) = 60
Since f(x) is an increasing function on [0, 5], we can conclude that for any value of x between 0 and 5, f(x) will lie between f(0) and f(5).
Therefore, there exists a value c in [0, 5] such that f(c) = 20.
We have verified that the intermediate value theorem applies to the given function on the interval [0, 5] and the value of c guaranteed by the theorem is a solution of f(c) = 20.