Question

can someone please help me with this question What is the minimum value of the quadratic function f(x) = x² - 2x + 7

Answer 1

minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).

Explanation:

Here we have , f(x) = x² - 2x + 7 or
`f(x) = x^2 - 2x + 7` . We need to find the minimum value of f(x) for which we need to differentiate it one time and equate it to zero . Value of x at which first differentiation of f(x) is zero will be the minimum value of function . Let's solve this:

`f(x) = x^2 - 2x + 7`

⇒
`f(x) = x^2 - 2x + 7`

⇒
`(df(x))/(dx) = (d(x^2 - 2x + 7))/(dx)`

⇒
`(df(x))/(dx) = (d(x^2))/(dx) - (d(2x))/(dx) + (d(7))/(dx)`

⇒
`(df(x))/(dx) = 2x-2 = 0`

⇒
`2x-2 = 0`

⇒
`x =1`

Now, value of function at x=1 is :

`f(x) = x^2 - 2x + 7`

⇒
`f(x) = x^2 - 2x + 7`

⇒
`f(1) = 1^2 - 2(1) + 7`

⇒
`f(1) = 8- 2`

⇒
`f(1) = 6`

Therefore, minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).