Question

(x-2)(x-9) minimum value

Answer 1

(x -2) (x -9)
= (x^2 2x - 9x + 18)
=(x^2 - 11x + 18)
= x^2 - 11x + 121/4 - 121/4 + 18
(x - 11/2)^2 - 49/4
x = 11/2 = -49/4

Answer 2

Answer:

Above function is minimum at $x=\frac{11}{2}$

Step-by-step explanation:

Given (x-2)(x-9)

we have to find the minimum value

To get the minimum value we have to differentiate the above polynomial and put it equals to 0 and then find the x value.

$f(x)=(x-2)(x-9)=x^2-11x+18$

$f'(x)=2x-11$

Now, equate f'(x) to 0

⇒ $2x-11=0$ ⇒ $x=\frac{11}{2}$

To check the above value whether it is maximum or minimum at the above value we have to double differentiate f(x).

f''(x)=2 which is positive.

Hence, above function is minimum at $x=\frac{11}{2}$