Final answer:
You can find the slope of a function at a given point by differentiating the function, which gives you a derivative. The derivative represents the slope of the function at any given point. By substituting the x-coordinate of the given point into the derivative, you can find the slope of the function at that point.
Step-by-step explanation:
To find the slope of a function at a given point, you would use the process of differentiation, a concept in calculus. Essentially, the slope of a curve at a point is equal to the slope of a straight line tangent to the curve at that point. This can be calculated using the derivative of the function. The derivative of a function can be thought of as a function that outputs the slope of the original function at any given point.
For example, if you have a function #f(x) = x^3#, the derivative of this function, represented as #f'(x)# or #(df/dx)#, is #3x^2#. If you want to find the slope at a point, say x=2, you plug this into the derivative and get #f'(2) = 3*(2)^2 = 12#. So, the slope of the function #f(x) = x^3# at x = 2 is 12.
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