Answer:
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum (or "no absolute maximum")
Step-by-step explanation:
There will be extremes at the ends of the domain interval, and at turning points where the first derivative is zero.
The derivative is ...
h'(t) = 24t^2 -48t = 24t(t -2)
This has zeros at t=0 and t=2, so that is where extremes will be located.
We can determine relative and absolute extrema by evaluating the function at the interval ends and at the turning points.
h(-1) = 8(-1)²(-1-3) = -32
h(0) = 8(0)(0-3) = 0
h(2) = 8(2²)(2 -3) = -32
h(∞) = 8(∞)³ = ∞
The absolute minimum is -32, found at t=-1 and at t=2. The absolute maximum is ∞, found at t→∞. The relative maximum is 0, found at t=0.
The extrema are ...
- (-1, -32) absolute minimum
- (0, 0) relative maximum
- (2, -32) absolute minimum
- (+∞, +∞) absolute maximum
_____
Normally, we would not list (∞, ∞) as being an absolute maximum, because it is not a specific value at a specific point. Rather, we might say there is no absolute maximum.
Number of boys enrolled is 105
<em><u>Solution:</u></em>
Given that, At a local preschool there is s as ratio of 3 boys to every 4 girls
There are 245 total preschoolers
Ratio of boys and girls = 3 : 4
Number of boys : number of girls = 3 : 4
Let the number of boys be 3x
Let the number of girls be 4x
Total number of preschoolers = 245
Therefore,
number of boys + number of girls = 245
3x + 4x = 245
7x = 245
x = 35
Number of boys = 3x = 3(35) = 105
Thus number of boys is 105
Answer:
Total amount Tara earned for babysitting for h hours = 8h
Step-by-step explanation:
Amount earned per hour for babysitting = $8.00
Number of hours of babysitting = h hours
Total amount Tara earned for babysitting for h hours =
Amount earned per hour for babysitting × Number of hours of babysitting
= 8 × h
= 8h
Total amount Tara earned for babysitting for h hours = 8h
I think that the length's area is 6075