Question

From the Mean Value Theorem for Integrals, we know that there is a c in (3,4) such that ????(c) equals this average value you just found. Find c. g

Answer 1

Answer:

1)$a$

2)$c=f'(c)\\f'(c)=\int_{4}^{3}f'(x)dx$

Step-by-step explanation:

Despite some missing part like the function, still we can affirm:

1) The Mean Value Theorem states that given a differentiable function f over an interval (a, b) [in this case (3,4)], then we know that there's a value "c" of between the endpoints of this interval.

And this c:

$a$

2) If c equals to the average value, then we can say that:

$c=f'(c)$

And

$f'(c)=\frac{1}{4-3}\int_{4}^{3}\frac{f'(x)}{4-3}dx\Rightarrow f'(c)=\int_{4}^{3}f'(x)dx$