To find the slope of the tangent line to the function \(f(x) = x^2 - 6x\) at the point (5, f(5)), we'll follow these steps:
1. Calculate the derivative of the function \(f(x)\) to find the slope of the tangent line at any point.
2. Plug in the x-coordinate, which is 5, to find the slope of the tangent line at that specific point.
So, let's start with step 1:
\(f(x) = x^2 - 6x\)
Now, calculate the derivative, \(f'(x)\), with respect to \(x\):
\(f'(x) = 2x - 6\)
Now, we have the derivative \(f'(x)\), which represents the slope of the tangent line at any point \(x\).
For step 2, we want to find the slope of the tangent line at \(x = 5\). Plug in \(x = 5\) into \(f'(x)\):
\(f'(5) = 2(5) - 6 = 10 - 6 = 4\)
So, the slope of the tangent line to the function \(f(x) = x^2 - 6x\) at the point (5, f(5)) is 4.