The volume of water (in liters) in a reservoir after t hours is given by the function V(t) for 0 < t < 10. The graph of the derivative V'(t) is shown below. V'(t) 2 6 -2 -4 After 10 hours, the volume of water in the tank was 51. What was the volume of water in the at t = 0? (Hint: Note that there was more water at the start than at the end.)

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: The derivative of a function is f'(x) x(x + 2)(x - 4). Find the value of x at each point %3D where…

A:

Q: Find the derivative of each function. a. f(x) = e³x f'(x) = b. f(x) = -8e³ f'(x) = c. f(x) = -4e0.5.…

A:

Q: 12. An airplane, travelling horizontally at a speed of 0.200 km/s passes directly above a radar…

A:

Q: Which derivative rule(s) was (were) usec f(x) = 2 e* + 7lnx - Vx3 1 7 f'(x) = 2 ex + 3. 4 4

A:

Q: 10. Question: Find h(2) . Assume f(1) = 2, ƒ(2) = 0, ƒ′(1) = 3, ƒ′(2) = 4 . g(x) is given by the…

A: To find . Assume . is the graph given below.

Q: Q4. As lava from a volcano cools, it flows more slowly. The distance the leading edge of the lava…

A: Consider the given function.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: