How do you find the maximum or minimum value of a function example?

HOW TO FIND MAXIMUM AND MINIMUM VALUE OF A FUNCTION

1. Differentiate the given function.
2. let f'(x) = 0 and find critical numbers.
3. Then find the second derivative f”(x).
4. Apply those critical numbers in the second derivative.
5. The function f (x) is maximum when f”(x) < 0.
6. The function f (x) is minimum when f”(x) > 0.

What is the minimum value of y x 2 4x 6?

y = 2
The minimum value, or the least value of y, of the quadratic equation y = x2 – 4x + 6 is y = 2.

How do you find the maximum Y of a function?

If you have the graph, or can draw the graph, the maximum is just the y value at the vertex of the graph. If you are unable to draw a graph, there are formulas you can use to find the maximum. If you are given the formula y = ax2 + bx + c, then you can find the maximum value using the formula max = c – (b2 / 4a).

How do you find the maximum and minimum of a function in calculus?

One of the great powers of calculus is in the determination of the maximum or minimum value of a function. Take f(x) to be a function of x. Then the value of x for which the derivative of f(x) with respect to x is equal to zero corresponds to a maximum, a minimum or an inflexion point of the function f(x).

What is the maximum or minimum value of the function what is the range Y =- 2x 32x 12?

The maximum or minimum value of the function y = -2×2 + 32x – 12 is (8, 116) and the range of the function y = -2×2 + 32x – 12 lies in the interval (−∞,116) .

Does the function have a maximum or minimum?

If the parabola opens upward, your answer will be the minimum value. If the parabola opens downward, your answer is the maximum value. In this example, since the parabola opens upward, f(-1.25) = 0.875 is the minimum value of the function.

How do you find the maximum or minimum value of two variables?

x = a is a maximum if f (a) = 0 and f (a) < 0; • x = a is a minimum if f (a) = 0 and f (a) > 0; A point where f (a) = 0 and f (a) = 0 is called a point of inflection. Geometrically, the equation y = f(x) represents a curve in the two-dimensional (x, y) plane, and we call this curve the graph of the function f(x).