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: derivative of the Find the > Fcx) = ¹² (x² +1) Following Function

A:

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.…

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

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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: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

Q: A. Find the derivative of each function. 1. f(x) = 26 2. g(x) = -9 3. f(x) = x+7 4. y = 4-2x 5. f(x)…

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.

Q: Given the function f(x) = 3cos(x/2), find the relative extrema on the interval (pi, 7pi) using the…

A: Given that: f(x)=3.cosx2       in (π, 7π)

Q: Compute for the derivative of the function below for x = 1. f(x) = 2xe

A: Solution: dydxx=1=2xex

Q: I. Find the derivative of the given function by definition f (s) = (5s" + 2)(2s" – 1) Where r is the…

A: Function:                          f(s)=(5sr+2)(2sr-1)   Here :                           r=4;

Q: y = 522 Find the Derivative - d/dx

A: we have to find the derivative of the following

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: