x²+4 Let: f(x)= - 16x f'(x) = - f"(x)= 16(3x2+4) x² –4° (x²–4)² ' (x² –4)° 5. Sketch the graph of f, label all important points from part (1), (2) and (3).

Q: Consider the function h(x) = 1/5 x^5 − 1/3 x^3 + 2. a)  Using derivatives, find the interval(s)…

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Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: pemplicit derivativeg 3 find y' if y is a function of x .

A: topic - implicit differentiation

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Q: Sketch the graph of f(x) = sin¬'(x² + y²) by analyzing its level curves.

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Q: ことる ーx (x+2)(X-2) -6x (x -ax+4) y" CX+2) (x-1)3 need first derivative Eanalysis %3D (x-2)3 (x+2)°

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Q: given the following information about its derivative: f'(x) -2 f'(x) = 0 at x = -2 -10

A: We will use relation between derivative  and character of the graph to draw

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

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Q: The y' for y = (x³ +

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Q: 4. Which graphs of ƒ may have a point of inflection? State the coordinates of each point a) ƒ''(-4)…

A: For a function f, if its second derivative f″(x) exists at x0 and x0 is an inflection point for f,…

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A: In the question it is asked to draw diagram for f(x)=x(x-3)(x+3). Also it is asked to draw…

Q: d. Consider the graph of y = f (x). Fill in the blanks: -3 -1

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Q: Considering the following graph of the given function f. y The xy-coordinate plane is given. The…

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Q: Find y" in terms of x and y. You must use implicit differentiation for this problem. 1- xy = x – Y

A: Given : 1-xy = x-y

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Q: the graph alongside to find

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Q: Find p′(t), p′′(t), and p′′′(t) for the function p(t) = t^(100)+ 4e^(t)+ 16. (You can use rules or…

A: The function is p(t)=t100+4et+16

Q: p(x) = (-2x)f(x), q(x)= f(g(x)), r(x)= 31 Use the table to find the derivative values. f(x) %3D

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