Answer:
a=2,b=4. (3a+b)=3*2+4=10.
Answer:
1) Both 15.
2) 25 and -25.
Step-by-step explanation:
1) Let the 2 numbers be x and 30 - x.
The product = x(30 - x)
f(x) = x(30 - x)
f(x) = 30x - x^2
Finding the derivative:
f'(x) = 30 - 2x
Finding the maximum:
30 - 2x = 0
x = 15.
This gives a maximum f(x) because f"(x) = -2.
So the numbers are 15 and 30 - 15 = 15.
2). If one number is x the other is y.
x - y = 50
y = x - 50
The product =
x(x - 50)
= x^2 - 50x
Finding the derivative:
2x - 50 = 0 for a minimum value.
2x = 50
x = 25.
So the numbers are 25 and 25-50 = -25.
Shifted up
For example: if f(x) = x^2 + 4, the parent function has a vertex at (0,0), but the +4 shifts the graph up 4 units on the y-axis so the vertex would be (0,4)
642+10= 652//////////////
