max is at vertex
in form 
the x value of the vertex is 
given, 
a=6, b=0
the x value of the vertex is -0/(2*6)=0
the y value is 
so vertex is at (0,-1)
since the value of a is positive, the parabola opens up and the vertex is a minimum value of the function
therefore that value is the smallest value the function can be
domain=numbesr you can use for x
range=numbesr you get out of inputting the domain
domain=all real numbers
range is {y | y≥-1} since y=-1 is the minimum
Answer:
-3x²-5xeˣ-eˣ
-3eˣx²-11eˣx-6eˣ
Step-by-step explanation:
I'm going to go by the picture and not what you wrote in your title.
To find the derivative of this we have to apply the product rule
(a*b)'=
a'*b+a*b'
We plug in our numbers and get
(-3x²+x-2)'*eˣ+(-3x²+x-2)*eˣ'
Now we can evaluate the derivatives and simplify
(-3x²+x-2)'= -6x+1
eˣ'=eˣ
which means we have
(-6x+1)*eˣ+(-3x²+x-2)*eˣ
Simplify
-6xeˣ+eˣ-3x²eˣ+xeˣ-2eˣ
Combine like terms
-3x²eˣ-5xeˣ-eˣ
Now we just need to find the derivative of this
We can apply the same product rule as we did before
(-3x²eˣ)'
Let's start by factoring out the -3 to get
-3(x²eˣ)'
which is equal to
-3(x²eˣ'+x²'eˣ)
Compute this and get
-3(x²eˣ+2xeˣ)= -3x²eˣ-6xeˣ
Now let's find the derivative of the second part
(-5xeˣ)'
-5(x'eˣ+xeˣ')
-5(eˣ+xeˣ)
-5eˣ-5xeˣ
Which means we have
(-3x²eˣ-6xeˣ)+(-5eˣ-5xeˣ)-eˣ
Combine like terms and get
-3eˣx²-11eˣx-6eˣ
200,000 milligrams is equivalent to 200 grams.
Step-by-step explanation:
P(t) = 12,000 (2)^(-t/15)
9,000 = 12,000 (2)^(-t/15)
0.75 = 2^(-t/15)
ln(0.75) = ln(2^(-t/15))
ln(0.75) = (-t/15) ln(2)
-15 ln(0.75) / ln(2) = t
t = 6.23
Answer: cotθ
<u>Step-by-step explanation:</u>
tanθ * cos²θ * csc²θ
= 
= 
= cotθ
Answer: B
<u>Step-by-step explanation:</u>
The parent graph is y = x²
The new graph y = -x² + 3 should have the following:
- reflection over the x-axis
- vertical shift up 3 units
Answers:
- a. Quadrant II
- b. negative
- c.
- d. C
- e.
<u>Explanation:</u>
a) Quadrant 2 is: 
b) In Quadrant 2, cos is negative and sin is positive, so tan is negative
c) 
=
d) the reference line is above the x-axis so it is negative --> 
e) 
