Question

1.- find the difference quotient for the following functions. (a) f(x) = 5x - 7

Explanation:

Step1: Recall the difference quotient formula

The difference quotient of a function \( f(x) \) is given by \( \frac{f(x + h)-f(x)}{h} \), where \( h
eq0 \).

Step2: Find \( f(x + h) \)

Given \( f(x)=5x - 7 \), substitute \( x\) with \( x + h \):
\( f(x + h)=5(x + h)-7=5x+5h - 7 \)

Step3: Substitute into the difference quotient formula

\( \frac{f(x + h)-f(x)}{h}=\frac{(5x + 5h-7)-(5x - 7)}{h} \)

Step4: Simplify the numerator

Simplify \( (5x + 5h-7)-(5x - 7) \):
\( 5x+5h - 7-5x + 7=5h \)

Step5: Simplify the fraction

Now, divide the simplified numerator by \( h \):
\( \frac{5h}{h}=5 \) (for \( h
eq0 \))

Answer:

The difference quotient is \( 5 \)