if ( f(x)=2x + 7 ), find ( \frac{f(a + h)-f(a)}{h} ).\nthe value of ( \frac{f(a + h)-f(a)}{h} ) for (…

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

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

Answer

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\neq0 ) (in the context of the difference - quotient formula), cancel out the ( h ) terms.

Answer:

( 2 )