Use calculus to show that the function, f (x) = x³ + 3x – 6, has exactly three zeros (where f(x) = 0) and that one zero is in (1, 2). i) Sketch the graph of f(x). Determine whether f(x) is ii) even or odd or neither, ii) decreasing or increasing or neither.

Q: A function is defined by z = x2y - xy2. Identify the independent and dependent variables.

A: Given function is

Q: Determine whether the equation xy - 5y = 1 defines y as a function of x.

A: Here we determine whether the equation xy-5y=1 defined y as a function of x.

Q: x²y" + 3ry – 24y = 0, y(1) = -8, y'(1) = –7. y =

A:

Q: DERIVE THE FF. FUNCTIONS: y.x(x-) 4x²+ 3x+2 %3D t.

A:

Q: Determine whether the equation y = -√(x + 4) defines y as a function of x.

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Q: 5- -4 -5 -4 -2 -3 -5 -5 0 -5 -4 -3 -2 2. ent

A:

Q: Determine whether the equation defines y as a function of x : x = y2

A: The given function is: The given function has to be y=f(x).

Q: Let X= {a,b} and Y={1,2,3}. Find the number n of functions from X into B

A:

Q: coming year. Total profit from planting xj acres at farm j is expressed by the function P(x,, X2,…

A: profit = 235x1 + 540x2 + 252x3 - 525000 we are given that x1 = 300 x2 = 600 x3 = 450

Q: Determine whether the equation x = y2 defines y as a function of x.

A: Consider the following equation: x=y2 For x>0 there are two values of y. Substitute x=4 in the…

Q: 1.) Determine if each equation is a function. a.) x - y = 5 b.) y=x²-3x + 5 c.) x² + y² = 16

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Q: a.) What is the domain of the function y =√x-4? b.) If f(x) = x^2 - 3x, find f(-1.8).

A:

Q: Draw the function of y = x 2 / 3 + x2

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Q: Determine whether the function x² +3 (x - 1)² is even, odd or neither. h(x) =

A:

Q: 1) Determine whether the equation defines y as a function of x. x = y3

A: Givenx=y3

Q: Let f(x)=x²+2 and g(x)=1-3x. Find each function value: 4)

A:

Q: Q2: Define whether y represent as a function of x a) -5x? + y = 12 b) -2x + y? = 3

A: