For f(x)=secπx4 , determine if the Intermediate Value Theorem applies on the interval [0,4] . If it does, find the value of c such that 0≤c≤4 and f(c)=12 . (1 point) Responses c = 0 c = 0 c=12 c = 1 2 c = 1 c = 1 c=32 c = 3 2 The Intermediate Value Theorem does not apply.
The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], and y is any value between f(a) and f(b), then there exists a value c in the interval [a, b] such that f(c) = y.
In this case, the function f(x) = sec(πx/4) is continuous on the interval [0, 4]. We need to determine whether the value 12 is between f(0) and f(4).
f(0) = sec(π(0)/4) = sec(0) = 1
f(4) = sec(π(4)/4) = sec(π) = -1
Since 12 is not between 1 and -1, the Intermediate Value Theorem does not apply on the interval [0, 4]. Therefore, there is no value c such that f(c) = 12 in this interval.