State the domain of the following functions:r(x) = 1/x^2-8x+15

Q: Find the slope of the secant line to the function f(x)=x3 when x=1 and x=2.

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Q: Find the derivative of the function.

A: Given  g(x)=3x2-22x+3-2 g(x)=2x+33x2-22 g(x)=2x+323x2-22 We use the following and differentiate g(x)…

Q: (1 – x) 2

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Q: Graph the piece-wise defined function. for x -1

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Q: Differentiate the function: f(x) = x44x

A: We assume u and v, then find u' and v'

Q: Determine the end (long run) behavior for the function below:   f(x)=x^4−3x^3+x−1

A: Solution ) f(x) = x4 - 3x3 + x - 1  We only see Degree of polynomial = 4 ( even )  Leading…

Q: Find the derivative of the function f(x)=(2x-7)/(3x-2)

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Q: Express the area A of a rectangle as a function of the length of the rectangle is twice its width

A: Topic:- Function

Q: Order the functions from slowest growing to fastest growing as x -o: 4x², (In x)³, 10*, and e2x

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Q: Differentiate the function: y= x^3 - 2x

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Q: Differentiate. 3 f(x)=x In 5x f'(x) =

A: The derivative of lnx is 1/x

Q: Match the function from the left side to its derivative. 1. x16 -4x-5 3 a. 2. 15 b. 3. ** 15x4 с.

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Q: 5. x²y3 5

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Q: Find the derivative of the function: f(x)= 16x5/4 + 8x-1/4 - 7x + 3

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Q: Differentiate the function with respect to the independent variable. f(x) = (6 - 5x²) ³ f'(x) =O

A: Given, fx=46-5x23

Q: find the interval where the function is increasing or decreasing  f(x) = 6/x-4

A: Function is not defined at x=4  there are two intervals where the function is defined   ( -∞,4 ) and…

Q: Graph the piecewise function defined by

A: To draw graph of fx=x+2       if x≤14             if x>1

Q: Differentiate the function. y = (x+2)(x² + 2x +1)

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Q: f(x) = 3 – 2x +x

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Q: Differentiate the function with respect to the independent variable. f(x)=-7x+5x³-6 f(x) =

A: Given, f(x)=-7x4+5x3-6

Q: Calculate the derivative of the function. f(x) = (2x2 – 9)-1

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Q: Apply the second derivative test to find the relative extrema of the function fx) =x*-18x-3

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Q: Calculate the derivative   f(x)=√(4+3x^2) / √(x^2+1)

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Q: A rectangular plot requires 2000 ft. of fencing to enclose it. If one of its dimensions is x (in…

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Q: sketch the graphof the function.y = 2−x2

A: Graph of the function can be drawn with the help of the points that lie on the curve. Substitution…

Q: Sketch f(x) = (x^2)/ (x^2 −5x+4) . Show all your work.

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Q: f(x) = (4x³ + 6x +1)°

A: To find the derivative of,  f(x) = (4x3 + 6x + 1)9

Q: Differentiate the function. f(x) = 270 "(x) =

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Q: Find the equation of the secant line on the graph of the function f(x)=7x2 between the points where…

A: take x=-1 . take x=5

Q: Find the derivative of f (x) = (x – 4) / 10x3 + 1.

A: Given,

Q: Find the derivative and simplify. f(x) = (x12 + 4x4 + 5)(2x3 - 1) f'(x) = %3D

A: Given : fx = x12 + 4x4 + 52x3 - 1

Q: Find the derivative f(x)=2x^5(√2x^5+5x^4)

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Q: Differentiate the function. fx) = (4 +x*)° - (1+x*) %3D f'(X) =

A: We have to find derivative

Q: Differentiate the functions. a) f(x) = 1– 2x +*

A: Given problem is  :

Q: Differentiate the function. f(x) = 16{x – 3 +2x

A: Given   f(x) = 16 x4-3+2x     now differentiating 1 w.r.t. 'x ' , we get    f'(x) = ddx16x14-3+2x…

Q: Find the slope of the graph of the function at the given value. f(x) = 4x+ 8. when x = 5 %3D

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Q: Find a linear function that approximate f(x) : 27. = x 3 near x =

A: To Determine: find a linear function that approximate f(x). Given: we have function fx=x23 near…

Q: Differentiate the function. f(x) = (5x2 – 7x)eX f'(x) =

A: →Product Rule of differentiation:                 duvdx = udvdx + vdudx→dexdx =ex→dxndx = n xn-1

Q: where is the function (5+x) / (x(x-2)) discontinuous?

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Q: Differentiate f(x) 2- 9x +5 f'(x) =

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Q: line to the functions: f(x)= v2 – 3x at x= -2 -

A: Definition used -                 Equation of a tangent to a point x= a for a function f(x) is…

Q: Determine the end (long run) behavior for the function below: f(x) = x* – 3x³ +x – 1

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Q: Determine the end (long run) behavior for the function below: f(x) = –2(x – 1)³(x+ 2)²

A: We first find the leading term of the given function  We will ignore the constants with the xs to…

Q: 14x

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Q: Express the area A of a rectangle as a function of the length x if the length of the rectangle is…

A: The area of the rectangle is given by the formula A=l×w where l is the length of the rectangle and w…

Q: Differentiate the function with respect to the independent variable. f(x) = - 3x° + 4x$ – 7

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Q: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0,8)…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.