Question

Ap calc multiple choice question; attached below please explain how, please!

Answer 1

Answer:

C. $\frac{f(b)-f(1)}{b-1}=20$

General Formulas and Concepts:

Calculus

• Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that  $f'(c)=\frac{f(b)-f(a)}{b-a}$

• MVT is also Average Value

Step-by-step explanation:

Step 1: Define

$f(x)=e^{2x}$

f'(c) = 20

Interval [1, b]

Step 2: Check/Identify

Function [1, b] is continuous.

Derivative [1, b] is continuous.

∴ There exists a c∈[1, b] such that $f'(c)=\frac{f(b)-f(a)}{b-a}$

Step 3: Mean Value Theorem

1. Substitute:                    $20=\frac{ f(b)-f(1)}{b-1}$
2. Rewrite:                        $\frac{ f(b)-f(1)}{b-1}=20$

And we have our final answer!