We've seen lines before. The restroom at half-time, the blue things on notebook paper...and they were all over algebra. y = mx + b, anyone? Lines are a special case of polynomials. Once we master them, we'll be ready to add some power. As in the power of 2. Not rangers.
Lines have a constant slope. If we write our line as y = mx + b, the slope will be m. But wait, isn't there a relationship between slope and derivative?
Yeah, they're kinda the same thing. Since lines have a constant slope the derivative of any line will just be m.
To recap, if f(x) = mx + b is a line, then f ' (x) = m. The derivative will be constant, and equal to the slope of the line for every value of x.
Exercise 1
Find the derivative of the function f(x) = 3x + 5.
Exercise 2
Find the derivative of the function f(x) = 2x.
Exercise 3
Find the derivative of the function f(x) where f is the line that passes through the points (4, 5) and (-1, -2).
.Exercise 4
Find the derivative of the function f(x) = 4.
Exercise 5
Find the derivative of the function f(x) = 7(x – 1) + 3.