Calculate the extreme values of x^2 + 6x - 6 .
Solution
To find the extreme values of x^2+6x-6.
We write x^2+6x-6 as (x^2+6x+3^2) -3^2 -6 = 0. We added here 3^2 and subtracted.
Therefore x^2+6x-6 = (x+3)^2 -9-5
x^2+6x-6 = (x+3)^2 -15.
x^2+6x-6 > A perfect square (x+3)^2 -15.
Therefore x^2+6x -6 is always greater than -15, as (x+3)^2 > 0 for all x and is minimum when
x+3 = 0 or x = -3.
Therefore x^2+6x-6 has the minimum (or extreme value) -15 when x = -3..
Calculate the extreme values of x^2 + 6x - 6 .SolutionTo find .pdf
1. Calculate the extreme values of x^2 + 6x - 6 .
Solution
To find the extreme values of x^2+6x-6.
We write x^2+6x-6 as (x^2+6x+3^2) -3^2 -6 = 0. We added here 3^2 and subtracted.
Therefore x^2+6x-6 = (x+3)^2 -9-5
x^2+6x-6 = (x+3)^2 -15.
x^2+6x-6 > A perfect square (x+3)^2 -15.
Therefore x^2+6x -6 is always greater than -15, as (x+3)^2 > 0 for all x and is minimum when
x+3 = 0 or x = -3.
Therefore x^2+6x-6 has the minimum (or extreme value) -15 when x = -3.
