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.
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.