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Maximas and minimas
Maximas and Minimas A maximum is the highest point a function can reach, and a minimum is the lowest point a function can reach. For a function to r...
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Maximas and Minimas A maximum is the highest point a function can reach, and a minimum is the lowest point a function can reach. For a function to r...
Maximas and Minimas
A maximum is the highest point a function can reach, and a minimum is the lowest point a function can reach.
For a function to reach a maximum, it must be increasing. For a function to reach a minimum, it must be decreasing.
To find the maximum or minimum of a function, we take the derivative and set it equal to zero. The point where the derivative is equal to zero is the critical point.
Critical points can be either maxima or minima. A critical point where the derivative is positive is a maximum, and a critical point where the derivative is negative is a minimum.
Examples:
A function f(x) = x^2 has a maximum at x = 0, and a function f(x) = x^3 has a minimum at x = 0.
The function f(x) = x^2 has a maximum at x = 2, and a function f(x) = x^3 has a minimum at x = -1