List the following quantities in order from least to greatest: f(-1-0.01)-f(-1) (1) -0.01 (II) the average rate of change of f on [-1, 1] (III) the instantaneous rate of change of f at r=1 (IV) f'(-1) (V) (2)-f(-1) 2-(-1) (VI) f(-1+0.01)-f(-1) 0.01

Q: f(x)=a? +bx+e The value of third derivative of the function is 6 at x=1. Find the value of a b) -1…

A: Given: f(x)=ax3+bx+c, whose third derivative of function is 6 at x=1 To find: The value of a

Q: Find the derivative of the function G(x) 1 + 2x3 – x2 + 5.3x + /10.

A: GIVEN:   G(x) = 12x4 + 2x3 - x2 + 5.3x + 10

Q: QUESTION 3 Let f(x) = ³1. (a) Find the average rate of change over [1,2]. (b) Find the average rate…

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Q: 7 -7 Use the fact that the derivative of the function f(x)= is f'(x) = - to find the equation of the…

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Q: What does this expression yield? J, f(x)dx The net area (signed area) between the graph of the…

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Q: 1960 to the beginning of 1964 is modeled by the function N(t) = 5.3e0.09312 -0.87t , for 0 <t< 4.…

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Q: 7. Consider the function f graphed below. 2 -4 4 -2

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Q: (a) Use the figure below to rank the quantities A = f'(1), B = f' (2), C =f'(3) from smallest to…

A: Derivatives by graph

Q: How do you solve question 9?

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Q: You are given the following function. 10t G(t) = t + 7 (a) Find the derivative of the function using…

A: The objective is to find the derivative of the function using definition and find domain of G(t) and…

Q: Use the given graph to estimate the value of each derivative. (a) F'(0) 0 (b) F'(1) 0 (c) f'(2) -1…

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Q: 15.lf the second derivative of f is given by f"(x) = x(x+3)(2 – x)² , then the graph of f has…

A: Given, The second derivative of f is given by f''(x)=x(x+3)(2-x)2 To find the inflection points of…

Q: Match the function with its graph. (a) f(x) = x (c) f(x) = Vĩ (b) f(x) = x' (d) f(x) = |x| I II III…

A: Functions and graphs

Q: Consider the following. x²-15 4-X (a) Find the derivative of the function, and check your work by…

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Q: 3) f(x) = 1+2 (a) Find f'(-2).

A: The given function isThe given point is

Q: Algebra Question

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Q: A (в C The graph of f', the derivative of the function f, is shown. Which of the following…

A: We need to choose correct option.

Q: 1(10,15) 2. An ant farm population is growing at a rate of g()=15e and declining at a rate of…

A: The rate of growth of an ant farm is gt=15e5t and  the rate of decline of the ant farm is dt=15e5t.

Q: f (x) f'(x) 4 -1 3 1 3 37. The table above shows certain values of the differentiable function f and…

A: We use product rule to find h'(x)