I really need help... factor by the simplest form 46xy^5
1 answer:
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<h2>Evaluating Composite Functions</h2><h3>Answer:</h3>
We can write how will be defined but that's too much work and it's only useful when we are evaluating
with many inputs.
First let's solve for first. As you read through this answer, you'll get the idea of what I'm doing.
Given:
Solving for :
Now we can solve for , since
,
.
Given:
Solving for :
Now we are can solve for . By now you should get the idea why
.
Given:
Solving for :
Answer:
a = 2, b = -2
P is at a minimum
Step-by-step explanation:
For any polynomial function, the turning point is either a maximum or a minimum
It can be determined by taking the first derivative of the function and setting it equal to 0 and solving for x and y
In this case we are given the turning point as x=1, y = 3 and we have to calculate a and b in the equation y = ax² + (ab)x + 5
The first derivative of y, y' = 2ax + ab
If we set this equal to 0 we get 2ax + ab = 0 ==> 2ax = -ab ==> b = -2
So the equation is of the form y = ax² -2ax + 5 (subbing for b)
Since we know that at x = 1, y =3 substitute y and x values in the above equation and solve for a
y = 3 = a(1²) - 2a(1) + 5
a - 2a + 5 = 3
-a + 5 = 3
a = 2
So the equation is of the form y = 2x² -4x + 5
If we plot this we will find that P is a minimum point
However, we can always determine mathematically if P is a max or min by taking the second derivative of the original function and noting the sign. If it is positive, the point is a minimum, and if it is negative, the point is a maximum.
Taking derivatives,
y' = 4x - 4
y'' = (4x-4)' = 4
The sign is positive so P is a minimum
Graph attached for reference
