Find a point 𝑐 satisfying the conclusion of the MVT for the given function and interval. 𝑦(𝑥)= √x , [36,144]

Answer 1

The MVT says (as long as the function is continuous and differentiable on the interval) that there is some value of x on the interval where the slope of the tangent line is the same as the slope of the secant line.

Here is a sketch of this:

Steps:

1) Find the slope of the secant line.

2) Find the derivative of f(x)

3) Set them equal and solve for "x"

The answer will be the value of "c"

Answer 2

Hey!

So, the first step to any MVT (Mean Value Theorem) problem is understanding the definition. Here, our interval that corresponds with [a,b] is [36,144]. Our denominator - by definition of b - a - is (144-36). Next to find f(b) - f(a), you just need to take the function evaluated at b and subtract it evaluated at a! In other words, our function (or f) is

√x.

Take the derivative of this function - it might be easier to write as x^1/2. Evaluate this at b first (144) then subtract it at a (36). These are also perfect squares so they should be easy to figure out. f(b) - f(a) will be your numerator. Simplify this quotient and it will give you your c!

Hope this helps!