Question

if $f(x) = 7x + 5$, find $dfrac{f(a + h) - f(a)}{h}$.

the value of $dfrac{f(a + h) - f(a)}{h}$ for $f(x) = 7x + 5$ is $square$.
(type an integer or a simplified fraction.)

Explanation:

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

Substitute \( x = a + h \) into \( f(x) = 7x + 5 \).
\( f(a + h) = 7(a + h) + 5 = 7a + 7h + 5 \)

Step2: Find \( f(a) \)

Substitute \( x = a \) into \( f(x) = 7x + 5 \).
\( f(a) = 7a + 5 \)

Step3: Compute \( f(a + h) - f(a) \)

Subtract \( f(a) \) from \( f(a + h) \).
\( f(a + h) - f(a) = (7a + 7h + 5) - (7a + 5) = 7a + 7h + 5 - 7a - 5 = 7h \)

Step4: Divide by \( h \)

Divide the result from Step 3 by \( h \) (assuming \( h
eq 0 \)).
\( \frac{f(a + h) - f(a)}{h} = \frac{7h}{h} = 7 \)

Answer:

7