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Scilla [17]
3 years ago
5

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

Mathematics
1 answer:
hodyreva [135]3 years ago
4 0

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

<u>Step-by-step explanation:</u>

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

⇒ \frac{df(x)}{dx} = \frac{d(x^2 - 2x + 7)}{dx}

⇒ \frac{df(x)}{dx} = \frac{d(x^2)}{dx}  - \frac{d(2x)}{dx}  + \frac{d(7)}{dx}

⇒ \frac{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).

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