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The image contains a math problem with a function \( f(x) = \frac{2}{x^2} \), and three sub-questions:

1. (a) \( f(4) \)
2. (b) \( f(22/a) \)
3. (c) \( \frac{f(3 + h) - f(3)}{h} \)

Let's solve each part:

### (a) Find \( f(4) \):
Given \( f(x) = \frac{2}{x^2} \), we substitute \( x = 4 \):
\[
f(4) = \frac{2}{4^2} = \frac{2}{16} = \frac{1}{8}
\]

### (b) Find \( f(22/a) \):
We substitute \( x = \frac{22}{a} \) into the function \( f(x) = \frac{2}{x^2} \):
\[
f\left(\frac{22}{a}\right) = \frac{2}{\left(\frac{22}{a}\right)^2} = \frac{2}{\frac{484}{a^2}} = \frac{2 \cdot a^2}{484} = \frac{a^2}{242}
\]

### (c) Find \( \frac{f(3 + h) - f(3)}{h} \) (difference quotient):
The difference quotient is given by:
\[
\frac{f(3 + h) - f(3)}{h}
\]
First, find \( f(3 + h) \):
\[
f(3 + h) = \frac{2}{(3 + h)^2}
\]
Now, find \( f(3) \):
\[
f(3) = \frac{2}{3^2} = \frac{2}{9}
\]
So, the difference quotient is:
\[
\frac{\frac{2}{(3 + h)^2} - \frac{2}{9}}{h}
\]
To simplify, combine the fractions in the numerator:
\[
\frac{2}{(3 + h)^2} - \frac{2}{9} = 2 \left(\frac{1}{(3 + h)^2} - \frac{1}{9}\right)
\]
Use a common denominator:
\[
\frac{1}{(3 + h)^2} - \frac{1}{9} = \frac{9 - (3 + h)^2}{9(3 + h)^2}
\]
Now substitute this into the difference quotient:
\[
\frac{2 \cdot \left(9 - (3 + h)^2\right)}{9(3 + h)^2 \cdot h}
\]

This expression can be further simplified depending on the specific limit process, but it represents the difference quotient for the given function.

Would you like more details or explanations for any part of this?

### Follow-up questions:
1. What is the limit of the difference quotient as \( h \to 0 \)?
2. How would you simplify \( f(22/a) \) for specific values of \( a \)?
3. Can we differentiate \( f(x) = \frac{2}{x^2} \) directly?
4. What is the graphical interpretation of the difference quotient?
5. How does the difference quotient relate to the derivative of the function?

**Tip**: The difference quotient is a fundamental concept in calculus, used to define the derivative of a function.

Let f(x) = 2/x^2. Find (and simplify as much as possible): (a) f(4), (b) f(22/a), (c) (f(3+h) - f(3)) / h.

Learn how to evaluate the function f(x) = 2/x^2 for specific values, including the difference quotient, with step-by-step solutions. This problem covers algebraic manipulation and calculus concepts. Suitable for Grades 10-12.

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