How to find the min and max of a quadratic function?

Quadratic functions are used in different fields of engineering and science to obtain values of different parameters. Graphically, they are represented by a parabola. Depending on the coefficient of the highest degree, the direction of the curve is decided.

Answer: By using differentiation, we can find the minimum or maximum of a quadratic function.

Let's understand this with the help of an example.

Explanation:

Let's take an example of quadratic equation f(x) = 3x² + 4x + 7.

Comparing with the general form of ax2 + bx + c = 0 , we get

a = 3, b = 4 , c = 7

Differentiating the function,

⇒ f'(x) = 6x + 4 

Equating it to zero,

⇒6x + 4 = 0 

⇒Therefore, x = -2/3

Double differentiating the function,

⇒f''(x) = 6 > 0

Since the double derivative of the function is greater than zero, we will have minima at x = -2/3, and the parabola is upwards.

Similarly, if the coefficient of x² is less than zero, then the function would have maxima.

Hence, by using differentiation, we can find the minimum or maximum of a quadratic function.

The maxima or the minima occurs at -b/2a.