1) The function is
3(x + 2)³ - 32) The
end behaviour is the
limits when x approaches +/- infinity.3) Since the polynomial is of
odd degree you can predict that
the ends head off in opposite direction. The limits confirm that.
4) The limit when x approaches negative infinity is negative infinity, then
the left end of the function heads off downward (toward - ∞).
5) The limit when x approaches positive infinity is positivie infinity, then
the right end of the function heads off upward (toward + ∞).
6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.
7)
x-intercepts ⇒ y = 0⇒ <span>
3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>
<span>⇒ (x + 2)³ = -1 ⇒ x + 2 = 1 ⇒
x = - 1</span>
8)
y-intercepts ⇒ x = 0y = <span>3(x + 2)³ - 3 =
3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 =
21</span><span>
</span><span>
</span><span>9)
Critical points ⇒ first derivative = 0</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒
x = - 2</span><span>
</span><span>
</span><span>ii)
second derivative: to determine where x = - 2 is a local maximum, a local minimum, or an inflection point.
</span><span>
</span><span>
</span><span>
y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an
inflection point at x = -2.</span><span>
</span><span>
</span><span>Using all that information you can
graph the function, and I
attache the figure with the graph.
</span>
Answer:
A) f(t) = 29,800(0.89)^t
Step-by-step explanation:The truck value decreases by 11% each year.
The present value of the truck was $29,800.
29,800 x 0.11 = 3,728 dollars lost from value.
29,800 - 3,728 = 26,522, the value of the truck after one year.
26,522 x 0.11 = 2,917.42 cash lost from value.
26,522 - 3,728 = 23,604.58, the value of the truck after two years.
Therefore, the answer is A) f(t) = 29,800(0.89)^t.
Answer:
2.
Step-by-step explanation:
The number of trees times 13
Answer:
D. 2.
Step-by-step explanation:
Using the points (1,3) and (-1,-1):
The slope= (3 - -1) / (1 - -1)
= 4/2
= 2.
Answer:
180 = 150m + c
177.25 mm
Step-by-step explanation:
L = mT + c
180 = m(150) + c
180 = 150m + c
c = 180 - 150m
181.5 = 210m + c
181.5 = 210m + 180 - 150m
1.5 = 60m
m = 0.025
c = 180 - 150(0.025)
c = 180 - 3.75
c = 176.25
L = 0.025T + 176.25
T = 40
L = 0.025(40) +176.25
L = 177.25 mn