Answers

1. The value of c by the Mean Value Theorem for Integrals for the function over the given integral is 6.25.

   In the question, we are asked to find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function f(x)=5√x,[4,9] over the given interval.

   The given function is f(x)=5√x,[4,9].

   First we calculate the function value at the endpoints of the interval.

   f(4) = 5√4 = 5*2 = 10.

   f(9) = 5√9 = 5*3 = 15.

   We substitute x = c in the given function, to get:

   f(c) = 5√c.

   Now, we calculate f'(c) using the formula:

   f'(c) = (f(b) – f(a))/(b – a),

   or, f'(c) = (f(9) – f(4))/(9 – 4),

   or, f'(c) = (15 – 10)(9 – 4),

   or, f'(c) = 5/5 = 1.

   Differentiating the original function, gives us f'(x) = 5/(2√x).

   Substituting x = c in this gives us f'(c) = 5/(2√c).

   Equating this to f'(c) = 1 gives us:

   5/(2√c) = 1,

   or, √c = 5/2,

   or, c = 25/4,

   or, c = 6.25.

   Thus, the value of c by the Mean Value Theorem for Integrals for the function over the given integral is 6.25.

   Learn more about the Mean value theorem at

   https://brainly.com/question/17111829

   #SPJ4

   The provided question is incomplete. The complete question is:

   “Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round your answer to four decimal places. Enter your answers as a comma-separated list.)

   f(x)=5√x,[4,9].”

   Reply