Final answer:
The difference quotient of the function f(x)=5x+7 is 5.
Step-by-step explanation:
The difference quotient is a mathematical expression used in calculus to approximate the derivative of a function. It is a key concept in understanding the concept of instantaneous rate of change and is an essential step in the development of the definition of the derivative.
To find the difference quotient, we need to evaluate the function f(x+h) and f(x), and then take the difference of these two values and divide by h. Let's substitute the values into the function: f(x+h)=5(x+h)+7=5x+5h+7 and f(x)=5x+7. Now we can calculate the difference quotient: (f(x+h)-f(x))/h=(5x+5h+7-5x-7)/h=5h/h=5.