Find the number c that satisfies the conclusion of the Mean Value Theorem:

Question

x^3+x-9 [0,2]

Answer 1

y = x^3 + x - 9
what is the change from 0 to 2 divided by 2?

y(2) = 8 + 2 - 9 = 1
y(0) = -9
change delta y = 1 -(-9) = 10
10/2 = 5 so somewhere between 0 and 2, dy/dx must be 5

dy/dx = 3 x^2 + 1
5 = 3 x^2 + 1
3 x^2 = 4
x^2 = 4/3
x = c = 1.15