write a formula for a function h(x), whose graph is identical to the graph of y=x^3 except that the graph of h has a hole at (2, 2^3). express the formula as a ratio of two polynomials

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: Use the chain rule to find the derivative of 12 3(-10x + 8x") You do not need to expand out your…

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Q: factor this derivative: 2/3x-1/3(x+4)2+x2/3 2(x+4). must show all steps

A: Solution -    Given equation -  f(x) = 23 x-13x+42+2 x23(x+4) = 0 f(x) = 2 x+423 x13+2 x23(x+4) = 0…

Q: Find the derivative using the Four-step rule f(x)=2x²-3x+4

A: let f(x) be any function then four-step process to computef'(x) = limh→0f(x + h) − f(x)h  by…

Q: Express the area A of an isosceles right triangle as a function of the length x of one of the two…

A: We have to express the area A of an isosceles right triangle   We have to write area as a function…

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x3 -…

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Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x2 -…

A: Given  The polynomial is  y = x2 - 4

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x2 +…

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Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: For k(x)=(x−1)(−x2−2x)(2x−2), find the derivative of k(x) using the product rule. Do not include…

A: Obtain the derivative of the function k(x) as follows.

Q: Write cosh(ln(x)) as a rational function of x.

A: Cos h (lnx)We knowCos h (a) = ea+e-qzsoCos h (ln x ) = elnx+ e-lnx2                       = x+1x2…

Q: sketch the graphof the function and state its domain. f (x) = 4 ln(x − 2) + 1

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Find the derivative. f(x) = 4/6x +7 f'(x) = %3D

A: As we know thatddxxm=ddxxm2=m2xm2-1

Q: . Approximate the negative root of the function using Secant method. 3x 9x + 5x + 2 = 0

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Q: Find the fifth derivative of (2x+3)5

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Q: Estimate L4 and R4 over [0, 3] for the function f(x) = 2x2. (Use decimal notation. Give your answers…

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Q: Find the derivative:   f(x) = (4x3-7x+9)5

A: Given:  fx=4x3-7x+95 To Find: The derivative of the given function

Q: use the chain of rule to differentiate f(x) = (x^10+ln(x))^10. What is the value of f^1(l)?

A: The given function f(x)=x10+ln x10

Q: Find the derivative of in two ways: first by applying the product rule and second by expanding the…

A: Applied product rule and found f'(x).

Q: Use the product rule to find the derivative of the function f ( x ) = ( x 2 - 3x + 2 ) ( 4 x 3 - x 2…

A: Given- fx=x2-3x+24x3-x2+4 To find- The derivative of the above function. Concept Used- The product…

Q: find the derivative by using the definition of a derivativef(x)=4x^2+1

A: Formula used:The derivative of f(x) with respect to x is the function f'(x) is

Q: Find the x-coordinates of all points where the graph of f(x) = 2x^3+9x^2-168x+21 has a horizontal…

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Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative.iii) y =…

A: Given: y=x3-3x2+4=(x+1)(x-2)2

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative.y = x3 -…

A: Axis interception points of x3-33x2+216x:  X Intercepts: 0, 0, 9, 0, 24, 0, Y Intercepts: 0, 0

Q: A closed rectangular box with a square base has a volume of 8000 cubic centimeters. Express the…

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Q: Next, differentiate the given function y = X 8x + 37 and write as a single fraction completely…

A: Derivative of function

Q: write cosh(4 ln x) as a rational function of x

A: To solve the given problem apply the following formula

Q: Find the second derivative  3x2/3/ 6x+ 9

A: Let the given function be y - y = 3x236x+9y = 12x23-1+9y = 12x-13+9Differentiating with respect to…

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

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Q: Find the areas below. a) Between the graph of f(x) = 50 + 3x² and x-axis over the interval [-2, 4].

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Q: A once-popular dog’s chew toy is slowly declining in popularity. The quartic function…

A: Given that x is the number of years since 1993 So 2001 means x=2001-1993=8

Q: The graph of a polynomial function, f(x), is shown above. In the interval shown, how many times with…

A: We know that for any functionfx, the second derivative of fx cross the x-axis means second…

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

A: Some differentiation formulae: ddx(xn)=nxn-1ddx(c)=0  ; c is any consant value Given function is…

Q: Differentiate the function. y = ln (square root of 5+8x/5-8x)

A: Given that: y=ln5+8x5-8x

Q: f '(x) by using the definition of the derivative. f(x) = 4 – 6x2

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Q: Find the slope of the secant line between x=3 and x=5 on the graph of the function f(x)=−2x^2+2x+5.

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Q: Does the graph of y = sqrt(x) - ln x, x> 0, have an inflection point? Try to answer the question…

A: To determine if the function has an inflection point.Part (a) By GraphingPart (b) By Calculus

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x3 -…

A: Find the zeros of a polynomial.

Q: For k(x)=(−3x2+2x−3)(x−2)(−x+3), find the derivative of k(x) using the product rule.

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Q: Find the average rate of change of f(x) = 7x² – 4 on the interval [3, b]. Your answer will be an…

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Q: Use the Product Rule to find the derivative of the function. f(x) = (5x − x3)(9x + 8)

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Q: Find the smallest positive root for the given function by using the false position method with…

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Q: 14x

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Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 − 4x + 2)(x3 − 5)

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Q: For k(x)=(3x+2)(−x+2)(−3x2+x+1), find the derivative of k(x) using the product rule.

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Q: Graph the tangent line to the function f(x) = –3x³ – 2x² – x + 3 at the point (-1, 5). Place point A…

A: Given that the function  is    f(x) = -3x3 - 2x2 - x + 3  Here we have to find the tangent line at…

Q: Find the second derivative of the polynomial functiony=2x5+3x4−4x3+x2−6.

A: Given Data The polynomial function is f(x)=2x5+3x4-4x3+x2-6.   Differentiate the polynomial function…

Q: Find derivative  of f (x) = 5x^6+75x^2-45

A: We have to find the derivative of  f(x) = 5x6 + 75x2 - 45

Q: Use the 2nd derivative to find the inflection point for f(x) = x³ – 6x² – 4x + 3

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Q: Express the area A of a right triangle as a function of the height h if the base of the triangle is…

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