182k views
0 votes
How to find the slope of a function at a given point

1 Answer

6 votes

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.

Learn more about Slope of Function

User Krono
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.