Difference quotient

Question

In College Algebra we begin to work with and simplify the difference quotient, which is given by the formula f(x+h)-f(x) over h. Find the difference quotient for the following function by completing the following steps: f(x)= -3x+7

a) find f(x+h)

b) find f(x+h)-f(x)

c) find and simplify f(x+h)-f(x) over h

Answer 1

a) f (x+h) = -3(x+h) + 7 , you simply substitute x+h for x in the equation

b) f(x+h)-f(x) = -3(x+h) + 7 - ( -3x +7) = -3x -3h + 7 + 3x - 7 = -3h

c) f(x+h)-f(x) / h = -3h / h = -3

What you just found is simply the derivative of the function f(x)= -3x+7 wrt to x or the slope of the tangent line to the curve which is in your case a straight line with slope of -3