Design a function that meets the following criteria: The function must have both a numerator and denominator. The function must be designed in such a way that when you find its derivative, you will need to apply the chain rule at some point. The function must be complex enough to demonstrate your understanding of the concepts from this unit. (ex: f(x)=1/(x-2)2 is not a sufficiently complex enough function).

Q: A1) Using the definition of derivative, find the derivative of f(x) = x² + 7x + 7.

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Q: The ideal weight w (in pounds) of a man is a function of his height h (in inches). This function is…

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Q: Find the derivatives of the following function f(x) from the first principles x4+4

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Q: Sketch the graph of the derivative for function shown.

A: Graph has a horizontal tangent between x=-2 and x=-1, at x=0 and at x=2.9, Therefore graph of f'…

Q: Direction: Let y-fpx). Note any pattern and use this to determine the derivative of the other…

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Q: For each function, sketch the graphs of the function when c = −3, −2, 1, and 2 on the same set of…

A: Note: According to the guidelines only one question will be answered. Please upload other…

Q: Plot g(x) = 2(x²-9) x²-4 Plot the asymptotes. Plot the y-intercept name it A (there's only 1), and…

A: We need to find asymptotes and intercepts then plot the graph and also it's derivative.

Q: Consider the function f(x) = 2x4 - 8x3. (a) Find the points, if any, at which the graph of each…

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Q: Consider the function 2x + 1 g(x) = x +1 a) Evaluate the derivative of the function. b) Sketch the…

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Q: Analyze using the tools of Calculus and sketch the graph of x3-1 f(x) = Otherwise write “none." Use…

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