Question

if ( f(x)=2x + 7 ), find ( \frac{f(a + h)-f(a)}{h} ).
the value of ( \frac{f(a + h)-f(a)}{h} ) for ( f(x)=2x + 7 ) is
(type an integer or a simplified fraction.)

Explanation:

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

Substitute \( x=a + h \) into \( f(x)=2x + 7 \).
\( f(a + h)=2(a + h)+7=2a+2h + 7 \)

Step2: Find \( f(a) \)

Substitute \( x = a \) into \( f(x)=2x + 7 \).
\( f(a)=2a+7 \)

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

\( f(a + h)-f(a)=(2a + 2h+7)-(2a + 7)=2h \)

Step4: Calculate \( \frac{f(a + h)-f(a)}{h} \)

Substitute \( f(a + h)-f(a)=2h \) into \( \frac{f(a + h)-f(a)}{h} \).
\( \frac{f(a + h)-f(a)}{h}=\frac{2h}{h} \)
Since \( h
eq0 \) (in the context of the difference - quotient formula), cancel out the \( h \) terms.

Answer:

\( 2 \)