Answer: Absolute minimum: f(-1) = -2
Absolute maximum: f(
) = 12.5
Step-by-step explanation: To determine minimum and maximum values in a function, take the first derivative of it and then calculate the points this new function equals 0:
f(t) = 
f'(t) = 
f'(t) = 
f'(t) = 
= 0
For this function to be zero, only denominator must be zero:
t = ±
≠ 0
t = ± 5
Now, evaluate critical points in the given interval.
t = 
and t = - 5 don't exist in the given interval, so their f(x) don't count.
f(t) =
f(-1) = 
f(-1) = 
f(-1) = 
f() = 
f() = 12.5
f(5) = 
f(5) = 0
Therefore, absolute maximum is f() = 12.5 and absolute minimum is
f(-1) = .
<span>3.12
First, write an equation to express what you know.
g = number of girls
b = number of boys
b * 2.52 + g * x = 2.88(b+g)
Solve for x, first substitute known values for g and b
12 * 2.52 + 18 * x = 2.88(12+18)
Add and multiply what you already know
30.24 + 18x = 86.4
Subtract 30.24 from both sides
18x = 56.16
Divide both sides by 18
x = 3.12
Therefore the GPA of the girls is 3.12</span>
Remember (a²-b²)=(a-b)(a+b)
solve for a single variable
solve for y in 2nd
add y to both sides
x²-7=y
sub (x²-7) for y in other equaiton
4x²+(x²-7)²-4(x²-7)-32=0
expand
4x²+x⁴-14x²+49-4x²+28-32=0
x⁴-14x²+45=0
factor
(x²-9)(x²-5)=0
(x-3)(x+3)(x-√5)(x+√5)=0
set each to zero
x-3=0
x=3
x+3=0
x=-3
x-√5=0
x=√5
x+√5=0
x=-√5
sub back to find y
(x²-7)=y
for x=3
9-7=2
(3,2)
for x=-3
9-7=2
(-3,2)
for √5
5-7=-2
(√5,-2)
for -√5
5-7=-2
(-√5,-2)
the intersection points are
(3,2)
(-3,2)
(√5,-2)
(-√5,-2)
16.5
Hope i was able to give the right answer
