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Derivatives of Linear Functions - Problem 1
As we've seen with finding instantaneous rates of change by finding the slope of a tangent line, the derivative of a function is the same as the slope of a tangent line, which is linear. So, to find the derivative of a linear function, simply find the slope of that function. For example, if f(x)=5-4x, recall that the formula of a linear equation is y=mx+b. So, the slope m of this example is -4. Therefore, the derivative of this function is -4.
Let's do a problem that involves the derivative of linear function. Now recall the formula; The derivative with respect to x of mx plus b is m, the slope of the line. Problem; find the derivative of each function, and use appropriate notation. So this will be good practice for us using our notation.
First, f(x) equals 2x minus 5. So f'(x) is going to be just m, whatever the slope is, in this case, 2. Part b y equals 3 minus x. This is the same as y equals -x plus 3. So you can see that the slope is -1. So I would say y' is -1.
Here, y equals 12, this is the same as y equals 0x plus 12. So the slope is 0, this is a horizontal line. You could say that y' is 0. You could also say dy/dx is 0. So these are two different notations for the same thing.