A person is standing and throws a ball into the air at time t = 0 seconds and from a height of 1 meter. The graph shows the height of the ball over time. The function f(t) = -(t – 3)² + 10 describes the motion of the ball. What is the average velocity of the ball over the interval 2, 3]? Ad 3 4 5 6 7 8 9 10 Time (sec) -2 meters per second O 1 meter per second O 3 meters per second O Average velocity cannot be calculated with the information provided. Height (m)

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Q: A ball is thrown into the air and its position is given by h(t) = - 5.5ť + 31t + 7 where h is the…

A: Given: h(t)=-5.5t2+31t+7

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Q: (B) Use the second derivative test to find the maxima and minima for f(2) = 22 - 15x + 1. 3 %3D

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Q: 4. Find the range of the function F(x)=√36-t² dt O [0, 36π] O [0, 18π] O [-6, 6] O [-6, 0]

A:

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Q: 9. Factor and sketch f (x) = -2x° – 10x + 18x + 162x³ + 216x² %3D b) State when the IROC is zero c)…

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Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x? – 12x + 5 b) Determine…

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Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

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A: The given function is: gy=y-1y2-3y+3 To find the critical numbers of the function.

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A:

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Q: The average rate of change of the function f() = 3x² + 7x - 5 on the interval (0, 3] is O 16 O 10…

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Q: Find the average rate of change of f (x) = 3x² – 4 over the following intervals. a) [0,3] b) [-4, 1]…

A: Average rate of change = f(b) -f(a)b-af(x) = 3x2-4a) (0,3) Average rate of change = f(3) -f(0)3-0…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.