Question

What important theorem is the key to proving the Fundamental Theorem of Calculus?

Short answer

The key to proving the Fundamental Theorem of Calculus is the Mean Value Theorem.

Step-by-step solution

Step 1. Given Information.

We have to find the objective which is the key to proving the Fundamental Theorem of Calculus.

Step 2. The theorem.

The key to proving the Fundamental Theorem of Calculus is the Mean Value Theorem.

The Mean Value Theorem is applied to anti-derivatives. It allows for relating the average rate of change of anti-derivatives to the instantaneous rate of change or the derivative of the anti-derivative.