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dondre54
25.06.2019 •
Mathematics
Find the value of x in the system, using substitution y=2x; 4x-y=-4
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Ответ:
x=-2
y=-4
Step-by-step explanation:
y=2x;
4x-y=-4
Substitute y =2x into the second equation
4x - (2x) = -4
4x - 2x = -4
Combine like terms
2x = -4
Divide by 2
2x/2 = -4/2
x=-2
Now we need to find y
y = 2x
y =2(-2)
y=-4
Ответ:
Find and classify the global extrema of the following function:
f(x) = 8 x^2 - 64 x
Find the critical points of f(x):
Compute the critical points of 8 x^2 - 64 x
To find all critical points, first compute f'(x):
d/( dx)(8 x^2 - 64 x) = 16 x - 64
= 16 (x - 4):
f'(x) = 16 (x - 4)
Solving 16 (x - 4) = 0 yields x = 4:
x = 4
f'(x) exists everywhere:
16 (x - 4) exists everywhere
The only critical point of 8 x^2 - 64 x is at x = 4:
x = 4
The domain of 8 x^2 - 64 x is R:
The endpoints of R are x = -∞ and ∞
Evaluate 8 x^2 - 64 x at x = -∞, 4 and ∞:
The open endpoints of the domain are marked in gray
x | f(x)
-∞ | ∞
4 | -128
∞ | ∞
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
The open endpoints of the domain are marked in gray
x | f(x) | extrema type
-∞ | ∞ | global max
4 | -128 | global min
∞ | ∞ | global max
Remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved:
x | f(x) | extrema type
4 | -128 | global min
f(x) = 8 x^2 - 64 x has one global minimum:
f(x) has a global minimum at x = 4