Answer:
Eyes
Step-by-step explanation:
I’m pretty sure
Answer:
Answer (e)
Step-by-step explanation:
Note that this graph has a zero at x = 1 and a vertical asymptote at x = -4. Only Answer (e) corresponds to that. Try letting x = 1. y is zero, correct? Try letting x = -4. y is undefined, correct?
Answer:
2.29 ft of side length and 1.14 height
Step-by-step explanation:
a) Volume V = x2h, where x is side of square base and h is hite.
Then surface area S = x2 + 4xh because box is open.
b) From V = x2h = 6 we have h = 6/x2.
Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.
We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.
Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.
To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.
And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2
f(x) = (x - 4)^2 - 5
Vertex (4 , -5)
This function opens upward and has min. value = -5
So range y >= - 5
So answer is A. -5 <= f(x) < ∞
