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weqwewe [10]
3 years ago
7

Helppppppppp pleaseeee Someoneeeee pleaseeee I neeed

Mathematics
1 answer:
Stella [2.4K]3 years ago
7 0

Answer:

The minimum value of f(x) is 2

Step-by-step explanation:

  • To find the minimum value of the function f(x), you should find the value of x which has the minimum value of y, so we will use the differentiation to find it
  • Differentiate f(x) with respect to x and equate it by 0 to find x, then substitute the value of x in f(x) to find the minimum value of f(x)

∵ f(x) = 2x² - 4x + 4

→ Find f'(x)

∵ f'(x) = 2(2)x^{2-1} - 4(1)x^{1-1} + 0

∴ f'(x) = 4x - 4

→ Equate f'(x) by 0

∵ f'(x) = 0

∴ 4x - 4 = 0

→ Add 4 to both sides

∵ 4x - 4 + 4 = 0 + 4

∴ 4x = 4

→ Divide both sides by 4

∴ x = 1

→ The minimum value is f(1)

∵ f(1) = 2(1)² - 4(1) + 4

∴ f(1) = 2 - 4 + 4

∴ f(1) = 2

∴ The minimum value of f(x) is 2

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