We first complete the square.
y=-x^2+2x+1
y=-x^2+2x-1+1+1
y=-(x-1)^2+2
The maximum point is (1,2) since -1 in ( ) meant 1 unit to the right and +2 meant 2 units up.
The maximum point is (1,2) but the maximum value means the y value which is simply just 2.
Done!
Answer:
(0,2)
Step-by-step explanation:
The solution would just be where these two functions cross, which is at the point (0,2) in this case.
This involves a quick application of the power rule, which is
![f'(x)=nx^{n-1}](https://tex.z-dn.net/?f=f%27%28x%29%3Dnx%5E%7Bn-1%7D)
.
First, it is helpful to rewrite
![f(x)=\sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%7Bx%7D)
as
![f(x)=x^{\frac{1}{2}}](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D)
. Remember that these are equivalent forms, but the latter is easier to use with the power rule.
We apply the power rule and simply:
Answer:
Your answer is option C … (-5, -1, 0)
Step-by-step explanation:
It is given in the question that
Ms. Velez will use both x gray bricks and y red bricks to build a wall around her garden. Gray bricks cost $0.45 each and red bricks cost $0.58 each. She can spend up to $200 on her project, and wants the number of red bricks to be less than half the number of gray bricks.
Maximum she can spend is $200. That is
![0.45x + 0.58y \leq 200 \\ y< \frac{1}{2} x](https://tex.z-dn.net/?f=0.45x%20%2B%200.58y%20%5Cleq%20200%0A%5C%5C%20%20y%3C%20%5Cfrac%7B1%7D%7B2%7D%20x)
And
![x\geq 0 , y \geq 0](https://tex.z-dn.net/?f=x%5Cgeq%200%20%2C%20y%20%5Cgeq%200)
And that's the required inequalities .