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.
Answer:
Megan is 14
Step-by-step explanation:
Megan is M
Molly is Mo
Mo = 8
M = x
6 + mo = x
6 + 8 = 14
Answer:
Step-by-step explanation:
3/9 = 1/3
xy^2/x^8y^6 = 1/x^(8-1)y^(6-2) = 1/x^7y^4
therefore, 1/3x^7y^4
Answer:
Step-by-step explanation:
Area of rectangle = length * width
= (3x + 2)(4x + 10)
= 3x *(4x + 10) + 2*(4x + 10)
= 3x *4x + 3x *10 + 2*4x + 2*10
= 12x² + <u>30x + 8x</u> + 20 {Combine like terms}
= 12x² + 38x + 20