A quadratic function f(x) = x3 + 3 x2 + 4 x + 3 has an inflectional tangent y = 2 x + 4 at ( -1 , 1 ). Determine the value of f( 1 ).

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: A manufacturer finds that the revenue generated by selling x units of a certain commodity is given…

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Q: The total-revenue and total-cost funtions for producing x clocks are R(x)=500x-0.01x2 and…

A: The total-revenue and total-cost functions for producing x clocks are The profit function is

Q: The equation of a quartic function with x-intercepts at 1 (order 2), -3 (order 1), 2 (order 1) and…

A: Let's find.

Q: For the function y = -2+5 sin (x-2), what is the maximum value?

A: Given,Function y =-2+5sinπ12(x-2)

Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

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Q: The function f (x, y) = 2x + 3y + 9 - x2 - xy - y2 has a maximum at some point (x, y). Find the…

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Q: The function f(x) = 2x3 – 42x? + 240x + 1 has derivative f'(x) = 6x² – 84x + 240. f(x) has one local…

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Q: Find the linearization of the function at a . f(x) = x 4 + 3 x2    , a = -1

A: We know that ,The linearization of the function at v=ais given by fa+f'ax-a

Q: Find the absolute maximum and minimum values of f(x) = 2x³ + 3z² + 7z – 5, if any, over the interval…

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Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 4x2 – 8x + 4 has a tangent…

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Q: The function f(x) = 2a* - 39x2 + 240x + 10 has derivative f'(x) = 6x² – 78x + 240. f(x) has one…

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Q: The quantity of the demand per month of a certain accessory is related to the price (in pesos) per…

A: Introduction: Differentiation has a wide range of applications in many fields of mathematics. One…

Q: Find all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

Q: Find the relative maxima and minima of y by the second-derivative test: (a) y = -2x2 + 8x = 25…

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Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x) =…

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Q: The revenue and cost function for a created of alarm clocks are about R(x)=520x-0.01x^2 and…

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Q: Find the quadratic approximation to g(x) = 1/x at x = 1. Graph g and its quadratic approximation…

A: Given function is,

Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: For what x does the function f (x) = 1/4 x2 - x + 2, 0 … x … 8, have its maximum value?

A: For a given function f(x) the critical point are the value of x at which the derivative of f(X)…

Q: Sketch a graph of the quadratic function. f(x) = x2 - 6x y y 10 10- 5- -10 10 -10 -5 5 10 5 10 10 y…

A: fx=x2-6x The graph is,

Q: Find a 4th degree function that has solutions X=-4-2/3 and x=-4+2/3, x=2i and x=-2

A: See the attachment

Q: Find the linearization of the function at x = 1.* f (x) 2x - 3x + 7 %3D

A: From the given problem:   fx=2x3-3x+7 ; x=1   As we know that the expression for linear…

Q: How can you display the values of a function ƒ(x, y) of two in-dependent variables graphically? How…

A: For a  function ƒ(x, y) of two in-dependent variables. It can be plotted graphed using 3d plotting…

Q: The total daily profit (in thousands of pesos)of a certain food company for the sale of ... x boxes…

A: Given:   Now, we need to find the value of x such that P(x) is the maximum. For simplicity, we plot…

Q: the total daily profit of a certain food company for the sale of boxes of buko is given by the…

A: Given: The total daily profit of a certain food company for the sale of boxes of buko is given by…

Q: For the function f(x) = x3 - 3x. Its local maximum is                 which occurs at ( Its local…

A: Given     fx=x3-3x

Q: Find the absolute maximum and absolute minimum y-values of the function f(x)= -12 + 4x - x2 on the…

A: The given function is parabola/ Quadratic form so this must contain absolute / relative maximum or…

Q: How to Find the quadratic function f(x)= ax2+bx+c that goes through (3,0) and has a local maximum at…

A: NOTE: Refresh your page if you can't see any equations. . the vertex form of the parabola is given…

Q: Find a quadratic function f (x) = ax2 + bx + c which has a vertex at (1, 1) and passes through (3,…

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Q: Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not more…

A: Consider the provided question, Yes, cubic function have at least one real root (x-intercept) but…

Q: The graph of f(x) = 2a² + 12z² – 72z + 14 has two horizontal tangents. One occurs at a negative…

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Q: 1. Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 - 4 / x - 2 are…

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Q: Show solution/process. 1. f(x) = 2x² – 4x + 5 at the point (–1,11) 2. f(x) = v25 – x² at the point…

A: Since there are more than one question, only one question can be answered. The function is given by,…

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: The quantity of the demand per month of a certain accessory is related to the price (in 500 0.01x²…

A: Given that the demand function is Px=5000.01x2+1. We have to find the number of accessories must be…

Q: 3. Find a linear approximation to the function at the point x = 3. y = f(x) = x²e + 8x

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Q: A goldsmith finds that the demand for gold is governed by p(x) = –x² + nx, where z is in (troy)…

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Q: Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not more…

A: Answer

Q: Find the maximum value of the function (x1 + 4.x2)² f(#1, x2) = by expressing f (x1, x2) as the…

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Q: The function f(x) = 2x³ − 33x² + 60x + 8 has derivative f'(x) = 6x² f(x) has one local minimum and…

A: Explanation of the answer is as follows

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

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Q: The function f(x) = 2x³ 24.x2 + 42x + 6 has derivative f'(æ) = 6x² – 48x + 42 - f(x) has one local…

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Q: Find a formula for the quadratic function whose y-intercept of y = 3 and x-intercepts at x = 1,…

A: Given: y-intercept y=3 x-intercept at x=1,4

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.