Find the local maximum and two local minima of the graph of the following function.
1 answer:
Answer:
max is (3, 1) and min are (2, 0) and (4, 0)
Step-by-step explanation:
Since there is no bounds on this (not a closed interval), the only max and min we can find are local. The max and min points exist where the first derivative of the function is equal to 0. That means that we have to find the first derivative. That is:
If you factor this higher-degree polynomial (I used the Rational Root Theorem and then synthetic division), you find that the zeros of the derivative exist at the x values of
2, 3, 4
Therefore, f(2), f(3), and f(4) will either be max values or min values.
f(2) = 0 so the point is (2, 0)
f(3) = 1 so the point is (3, 1)
f(4) = 0 so the point is (4, 0)
As you can see, the max point is (3, 1)
the min points are (2, 0) and (4, 0)
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Answer:
The man will take 64 seconds to reach to the south shore of the frozen pond.
Step-by-step explanation:
Given:
Weight of the man = 748 N Mass of the man, =
=
kg
Radius of the pond = 4 m
Mass of the textbook = 1.2 kg
Velocity at which the textbook is thrown = 4 ms^1
We have to find the velocity of the man after the throw.
Let the velocity is .
Now using law of conservation of momentum we can find the value.
Considering
And initial velocity of both the man and book i.e
So,
⇒
⇒ Plugging the values.
⇒
⇒
⇒ ms^-1
Here the negative velocity is meant for opposite direction of the throw.
Numerically we will write,
With this velocity the man will move towards south.
We have to calculate the time taken by the man to move to its south shore.
And we know
Let the time taken be and
and
then,
Then
⇒
⇒ Plugging the values.
⇒
⇒ sec
The man will take 64 seconds to reach to the south shore of the frozen pond (circular).