Recall there are three ways to estimate the derivative (or the rate of change) of a given function f(x) when we ONLY know a table of values of f(x). We have the: Forward Difference formula Backward Difference formula Central Difference formula Consider a particle moving on a straight line. Its displacement s(t) from a fixed point O on the straight line is given by the table of values below. t 0.5 1.0 2.0 2.5 3.0 3.5 s(t) | -4.0 -2.0 -1.0 1.2 1.8 2.2 la. Give all possible estimates for the instantaneous velocity at t = 0.5. State which estimate you apply.

Q: Use the function below to answer parts (a)-(c). f(x) = x² - 3 (a) Use the formal definition to find…

A: To Determine: a) use the formal definition to find the derivative of y=f(x) at x=2. b) find f(2) and…

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A: We are answering only the first three subparts as per our honor code. The graph of the derivative of…

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Q: An object is dropped off a building. Ignoring air resistance, the height above the ground t seconds…

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A: Given that the derivative is F(x) = x2   So, we have to find the antiderivative of F(x)

Q: -1 position (s, cm) 153 10- 5+ 0 2 3 4 time (t, seconds) 5

A: Slope of position(s) graph gives speed. i.e. Speed =dsdt

Q: Find the slope of the graph of the function at the given point. Re) = t=3; G8) Use the derivative…

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Q: 3x Suppose h(x) = (:) What is the correct result of the derivative of h with respect to x? · In (5)…

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Q: Find the derivative of the function. HINT [See Examples 1 and 2.] g(x) = x−2 − 5x−1 − 6

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Q: a. Find the derivative function f' for the following function f. b. Find an equation of the line…

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Q: Some values of a function f(x) and its derivative f' (x) are given below. 1 f(x) f' (x) -3 -1 4 2 6…

A: Chain rule of differentiation: also,

Q: hich of the following notions is closely related to the derivative of a function? a. slope b. zero…

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Q: Because the derivative of a function represents both the slope of the tangent to the curve and the…

A: For part a).   f'(x) >0                         Answer : a, b, d   For part b).   f'(x) <0…

Q: Calculate the derivative of the function. HINT [See Example 1.] f(x) = 1/3x-1   f '(x) =

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Q: Let f(x) = Vx +1. Calculate the difference quotient f(15 + h) - f(15). for h h = .1 h = .01 h 3= .01…

A: Given: f(x)=x+1 We have to find f(15+h)-f(15)h for h=0.1, 0.01, -0.01, -0.1 For h=0.1:…

Q: Some values of a differentiable function f and its. derivative are given below. 2 8. fG)…

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Q: Find the derivative of the given function. f(x) = (6 - 5x)-2 %3! 30x2 f'(x) = (-öx" + 6)3 What is…

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Q: Consider the following. p(q) = 3q2 + q + 3 (a) Find the derivative, by using the definition. p'(q)…

A: Slope of tangent = derivative at the given point

Q: Jse the figure below and the chain rule to estimate the derivative. The graph of f (x) has a sharp…

A: Here we have, f(x) has a sharp corner at x=6  and the graph of f(x) and g(x) is ,

Q: Use the function h(x) = 10/a + 2 to complete the problems given below. a) Find the average rate of…

A: To solve the problem we first calculate the rate of change of h(x) on the given interval then we…

Q: Which of the following are accurate descriptions of the second derivative of f (x)? Choose ALL that…

A: All the possible description about the second derivative of the function fx are given as following

Q: The graph of function f(x) is shown below. At which value of z is the derivative of the function…

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Q: 1. Using the definition of derivative, find the derivative of the follow HomeworK: functions: (a) y=…

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Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: We know that d/dx(xn)=nxn-1

Q: Let p(x) = x² sec(x)-x cot(x). Find the instantaneous rate of change of p at the point where Compute…

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Q: 6. Use the graph of the function f below to answer the following y = f(x) (a) draw the tangent line…

A: Note: There are multiple sub questions. No specific question has been asked. So, We will solve the…

Q: Let `h (x) = -3tan^5(-7x)` Determine the derivative of 'h`. (I 'h'(x)=' Determine the slope of `h`…

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Q: Below is the graph of the derivative of some function. 1.5A 15 (a) Sketch the graph of a possible…

A: For the solution of the problem follow the next steps.

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A: Given function is: - part(a): - First we have to plot the graph and an accurate one and for which…

Q: Cumulative Interest in Fidget Spinners 1000 900 800 700 600 50 400 300 200 100 20 20 30 40 50 60…

A: F'(w) will represent the slope of tangent to the curve.

Q: Use forwards, back ward and centered difference approach to approximate the derivative of the f (x)…

A: Given function is  fx=x2+9x-10

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Q: Evaluate the derivative of the function at the given point. c=6/5 - 9; s= 25 c'(25) = (Type an…

A: We have to find

Q: 5. The graph of y = f '(x), the derivative of f(x), is shown below. Given f(2)= 8, evaluate f(-2). 0…

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Q: Use the figure below and the chain rule to estimate the derivative. The graph of f (x) has a sharp…

A: Differentiability of composite function

Q: We need to think backward here: What function do we know has a derivativeequal to the given…

A: Given function,H(x)=lnx +e2xwe have to find a function has a derivative equal to the given function.

Q: (a) Find by definition, the derivative with respect to x of given function: f(x) %3 3 х3 +3

A: The derivative of fx with respect to x is the function f'x , which is defined as f'x = limh→0fx+h -…

Q: 1. Math the description of f(x) with the graph of its derivative f'(x) in the below figures. Give…

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Q: e Find the derivative of the function g(x) = 3+ 5x g'(x) = > Next Question

A: We have to find the derivative of  g(x)=ex3+5x

Q: Suppose the derivative of a function f is given below. On what interval is f increasing? (Enter the…

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Q: Let f(x) = √x + 6. Calculate the difference quotient f(10+h)-f(10) for h h = .1 h = h= h = .1 If…

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Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: The graph of gʻ(x), the derivative of a function g(x) is pictured below on the closed interval…

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Q: , Use the figures below to evaluate the indicated derivative, or state that it does not exist. If…

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Q: Use limits to find the derivative function ƒ′ for the followingfunctions f.b. Evaluate ƒ(a)for the…

A: ft=1t a).…

Q: Use the function below to answer parts (a)-(c). f(x) = x? - 2 (a) Use the formal definition to find…

A: Given: fx=x2-2

Q: Find the derivative of the function. HINT [See Examples 1 and 2.]   h(x) =  7/ x −  2/ x3 +  1/ x4…

A: The given function hx=7x-2x3+1x4      =7x-1-2x-3+x-4 Differentiate with respect to x using the…

Q: A manufacturer produces bolts of a fabric with a fixed width. The cost of producing x yards of this…

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Q: Use the function below to answer parts (a)-(c). f(x) = x? +6 (a) Use the formal definition to find…

A: The given function is, f(x)=x2+6. a) Find the derivative of y=f(x) at x=2 as follows. By definition…

Q: If the current position of the object at time t is s (t), then the position at time h later is s (t…

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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.