I will give you the crown if you answer this.
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Yes. In fact, that is basically the definition of a derivative. It is the instantaneous rate of change of a function.
For example, picture the graph of the following function:
The slope is constantly changing at every x-value, so to find the slope at x=a, we find the derivative of the function.
Once we have the derivative, simply plug in a for x to find the slope of the line tangent to f(x) at x=a.
For example, at x=5:
The slope of f(x) at x=5 is 10.
For example, picture the graph of the following function:
The slope is constantly changing at every x-value, so to find the slope at x=a, we find the derivative of the function.
Once we have the derivative, simply plug in a for x to find the slope of the line tangent to f(x) at x=a.
For example, at x=5:
The slope of f(x) at x=5 is 10.