# Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval if #f(x) = 2x^2 − 3x + 1# and [0, 2]?

##### 1 Answer

Apr 2, 2015

**The Mean Value Theorem** says that

if a function

then there exists a value

(The right hand side of this is often referred to as the **secant**).

For the given function

If we (temporarily) assume the Mean Value Theorem holds then there must be a value

which solves as

Testing this back in the equation of the Mean Value Theorem demonstrates that the theorem holds for the given equation.