if f(x)=5x + 6, find f(a), f(a + h), and the difference quotient of f, (f(a + h)-f(a))/h. completely…

Explanation:

Step1: Find f(a)

Substitute x = a into f(x). $f(a)=5a + 6$

Step2: Find f(a + h)

Substitute x=a + h into f(x). $f(a + h)=5(a + h)+6=5a+5h + 6$

Step3: Find the difference - quotient

Substitute f(a + h) and f(a) into the difference - quotient formula. [ \begin{align*} \frac{f(a + h)-f(a)}{h}&=\frac{(5a + 5h+6)-(5a + 6)}{h}\ &=\frac{5a+5h + 6-5a - 6}{h}\ &=\frac{5h}{h}\ &=5 \end{align*} ]

Answer:

$f(a)=5a + 6$ $f(a + h)=5a+5h + 6$ $\frac{f(a + h)-f(a)}{h}=5$