Question

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for the function \\(f(x) = 9x - 5\\), construct and simplify the difference quotient \\(\frac{f(x + h) - f(x)}{h}\\).

the difference quotient for \\(f(x) = 9x - 5\\) is .

Explanation:

Evaluate the function at x + h

$$ f(x+h) = 9(x+h) - 5 = 9x + 9h - 5 $$

Substitute into the difference quotient formula

$$ \frac{f(x+h) - f(x)}{h} = \frac{(9x + 9h - 5) - (9x - 5)}{h} $$

Simplify the numerator and divide by h

$$ \frac{9x + 9h - 5 - 9x + 5}{h} = \frac{9h}{h} = 9 \quad (h eq 0) $$

Answer:

The difference quotient for \(f(x) = 9x - 5\) is <blank>9</blank>.