Answer:
The value of c that satisfies the conclusion of the Mean Value Theorem applied to f on the interval [1,4] is approximately 0.1793.
Step-by-step explanation:
Given f(x) = 5cos²x² + ln(x + 1) - 3
The Mean Value Theorem applied to f on an interval [a, b] is given as
f'(x) = c = [f(b) - f(a)]/(b - a)
= [f(4) - f(1)]/(4 - 1)
c = [f(4) - f(1)]/3
f(4) = 5(cos4²)² + ln(5) - 3
= 3.2296
f(1) = 5(cos1²)² + ln(2) - 3
= 2.6916.
c = (3.2296 - 2.6916)/3
= 0.538/3
≈ 0.1793
I believe it is C but I haven’t done these problems for a while