Rewrite the given equation as
.
Since
, you can conclude that the imimum value of y will be gained for the minimum value of
. The minimum value of
is 0 for x=2.
So, y(2)=0+4=4.
Answer: minimum value of y is 4, when x=2.
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
There are 16 ounces in 1 pound: 5*16=80
80 ounces divided by 8 ounces gives you 10 8 ounce servings
Answer:
Infinite Solutions
Step-by-step explanation:
The lines overlap each other.
