Question

find the minimum value of x square +2bx+ c is

Answer 1

Let f(x)=x^2–5x+21

If we see geometrically, this is an upward parabola as coefficient of x^2 is positive.

Since it is an upward parabola, therefore it will always attain the minimum value.

Differentiate this function

f’(x)=2x-5

Equate it with 0, you will get that the function attains its minimum value at x=5/2.

On calculation f(5/2)=59/4.

Since the minimum value is postive, so taking modulus of this function will not change anything. Thus the minimum value of |f(x)| is also 59/4.




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