# 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# .