Set the first derivative of the function equal to zero,
and solve for the variable.
Chat with our AI personalities
Find the maximum and minimum values that the function can take over all the values in the domain for the input. The range is the maximum minus the minimum.
The general procedure is to find the function's derivative, and then solve for (derivative of the function) = 0. Each of these solutions may be a local maximum or minimum - or none. Further analysis is required. A local maximum or minimum may also occur at points where the derivative is undefined, as well as at the function's endpoints (assuming it is only defined for a certain range, for example, from 0 to 10).
y=2x2-3x2-12x+5=0
You didn't specify the equation. A minimum or maximum value of a function is often found by calculating the derivative of a function, writing an equation for derivative equal to zero, and then analyzing points where the derivative either doesn't exist, or is equal to zero. You'll find find information about this in introductory calculus books.
Differentiation lets you find the rate of change of a function. You can use this to find the maximum or minimum values of a differentiable function, which is useful in a lot of optimization problems. It's also necessary for differential equations, which are useful just about everywhere.