How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x) = x^3 + x^2# on the interval [0,1]?
1 Answer
Find all solutions to
Explanation:
So you need to solve
This won't factor easily, so use the quadratic formula or complete the square to get
# = (-2 +- sqrt(4+24))/6#
# = (-2 +- sqrt(28))/6#
# = (-2+- 2 sqrt7)/6#
# = (-1+-sqrt7)/3#
Sinced
We know that
#-1+2 < -1 + sqrt7 < -1 + 3# and
# 1/3 < (-1+sqrt7)/3 < 2/3# .