Answer:
Step-by-step explanation:
We are given an equation of circle with radius of 5 units:
To find the second derivative, you'd have to <u>differentiate</u> the equation <u>twice</u>.
We can use <u>implicit differentiation</u> to differentiate. Its concept is to derive like a normal for both sides of equation but since we are differentiating with respect to x and we have y-term, we derive normally then multiply by dy/dx or y'.
For simple clarification, you derive normal and <u>apply chain rules</u>. Hence why there's dy/dx multiplied by 2y:
Recall the power rules:
Chain Rules:
Hence:
<em>Note that deriving a constant will always result in 0.</em>
Simplify:
Solve for dy/dx:
We've finally found the first derivative of relation. However, we have to find the second derivative, so we derive dy/dx to find the second derivative:
Therefore:
For this, we will be using quotient rules. Keep in mind that both x and y are function!
Recall quotient rules:
Let u = -x and v = y:
Now we know that dy/dx = -x/y, so we substitute dy/dx as -x/y in the second derivative:
Simplify:
More simplification:
Therefore, the second derivative is:
Use y=mx+b
m = 4
x = 0
y = -1
-1 = (4)(0) + b
^^^
Multiply
Answer:
Decay.
Step-by-step explanation:
The reason for, is that growth is pointed up and decay is pointed down.
:)
Answer:
pretty sure is accociatve property
I sure it’s the second one