The absolute minimum = -2√2.
The absolute maximum= 4.5
Consider f(t)=t√9-t on the interval (1,3].
Find the critical points: Find f'(t)=0.
f"(t) = 0
√9-t² d/dt t + t d/dt √9-t²=0
√9-t² + t/2√9-t² (-2t)=0
9-t²-t²/√9-t²=0
9-2t²=0
9=2t², t²=9/2, t=±3/√2
since -3/√2∉ (1,3].
Therefore, the critical point in the interval (1,3] is t= 3/√2.
Find the value of the function at t=1, 3/√2,3 to find the absolute maximum and minimum.
f(-1)=-1√9-1²
= -√8 , =-2√2
f(3/√2)= 3/√2 √9-(3/√2)²
= 3/√2 √9-9/2
=3/√2 √9/2
=9/2 = 4.5
f(3)= 3√9-3²
= 3(0)
=0
The absolute maximum is 4.5 and the absolute minimum is -2√2.
The absolute maximum point is the point at which the function reaches the maximum possible value. Similarly, the absolute minimum point is the point at which the function takes the smallest possible value.
A relative maximum or minimum occurs at an inflection point on the curve. The absolute minimum and maximum values are the corresponding values over the full range of the function. That is, the absolute minimum and maximum values are bounded by the function's domain.
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for A. the cost is increasing $800 per ton
for part B hold up a sec
Answer:
A. (-10,18); 412 yards
Step-by-step explanation:
Answer:
2 hours 1 minute 9.23 seconds
Step-by-step explanation:
Since they are traveling in opposite directions, their separation speed is the sum of the magnitudes of their speeds: 30 +22 = 52 mph.
The time is related to speed and distance by ...
time = distance / speed
= (105 mi)/(52 mi/h = 2 1/52 h ≈ 2 h 1 min 9.23 sec
It will take a little over 2 hours before they are 105 miles apart.
Answer:
Step-by-step explanation:
180-117 = 63(l.p)
66+63+x = 180 ( angle sum property)
180 - 129 = 51
x = 51