Question

for the function f(x)=-2 : (a) a simplified form of the difference quotient (\frac{f(x+h)-f(x)}{h}), when (h
eq 0) (b) use the simplified form to compute...

Explanation:

Step1: Find \( f(x + h) \)

Given \( f(x)=-2 \), since it's a constant function, \( f(x + h)=-2 \).

Step2: Substitute into difference quotient

The difference quotient is \( \frac{f(x + h)-f(x)}{h} \). Substitute \( f(x + h)=-2 \) and \( f(x)=-2 \):
\[
\frac{-2 - (-2)}{h}
\]

Step3: Simplify the numerator

Simplify \( -2 - (-2) \): \( -2 + 2 = 0 \). So the expression becomes \( \frac{0}{h} \) (where \( h
eq0 \)).

Step4: Simplify the fraction

Since \( h
eq0 \), \( \frac{0}{h}=0 \).

Answer:

\( 0 \)