Question 7(Multiple Choice Worth 1 points)
1 answer:
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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) - 4(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
Without needing the distance formula
from 4,1 to 0,1, you move the "x" from 4 to 0, over the same "y" value of 1, so is just 4 units long, from the center to an endpoint, and the chord that stems from the center to an endpoint is the radius, so r = 4
from 4,1 to 0,1, you move the "x" from 4 to 0, over the same "y" value of 1, so is just 4 units long, from the center to an endpoint, and the chord that stems from the center to an endpoint is the radius, so r = 4