5. True or False The x-intercepts of the graph of a function y = f(x) are the real solutions of the equation f(x) = 0.

Q: 4. Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not…

A: 4. cubic equation must have at least 1 real solution so it must have cut the x-axis once since if…

Q: 1. A company manufactures and sells a televisions per month. If the cost and the revenue functions…

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

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Q: Given the piecewise function: 4x + 12 { x<-2 - 1<x f(x) = -2x + 6 18. What is the interval of the…

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Q: True or False The x-intercepts of the graph of a function  y = f(x) are the real solutions of the…

A: We know that the points where the graph of a function y = f(x) intersects the x-axis give the zeroes…

Q: If the total revenue function for a blender is R(x) = 28x − 0.01x2 where x is the number of units…

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Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

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Q: Q1/a- Write an equation of the Line that passes through point: P1 (-2,0), P:(2,-2)? b- find any locl…

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Q: The graph of f(x) passes through the point (-1,4), The slope of the line tangent to the graph at the…

A: The slope of the tangent of the function at a point is given by the derivative of the function at…

Q: 6. If two functions f (x) and g(x) have positive slope at x = a, must the function h(x) = f (x)g(x)…

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Q: Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where…

A: Step:-1 Note:-  your cost expression is not clear here as it can be 5a+b4v3   or   5a+b4v3 , So i am…

Q: The graph of the function y = f(x) passes through the point (-1, 1) and the line tangent to the…

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Q: Does the given equation define an implicit function around the point (y=3, x=1) and why?

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Q: how would you find the x-values that the function f(x) = 2e^x - 6x have horizontal tangent lines? I…

A: The given function fx=2ex-6x

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

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Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: If (0,8) is the y-intercept of f(x) and the slope of f at x is m(x)= 4x/(x^2+1)^3, then what is…

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Q: am having trouble finding the equation of the line tangent to the graph of f at (1,1), where f is…

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Q: 7. Given the profit function P(x) = 500x –- where 100 x is number of units sold. Find x to get…

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Q: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

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Q: 4. Find the point on the graph of f(x) 5x2 + 20x – 3 where the tan gent line is horizontal. (a)…

A: We have to solve integration

Q: 13. The revenue from a manufacturing process (in millions of dollars) is projected to follow the…

A: R(t) = 100+0.08 t C(t) = 60+0.2 t2   P(t) = R(t)- C(t)       = 100 +0.08 t -60 - 0.2 t2 P(t) = -0.2…

Q: 5. Determine the area of the largest triangle that can be formed in the first quadrant by the…

A: The area is found by making a function of area into a variable and finding the values at which…

Q: 4. a) Find the value of x where the function f(x) = (x – 4)5 is not differentiable.

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Q: How many critical points does the function f(x)=∣∣x3−12x∣∣ have?

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Q: 2. For what values of x does the graph of f(x) = x³ + 3x² + x + 3 have a horizontal tangent line.

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Q: 1. The minimum point on the graph of the equation y = f(x) is (2, – 1). If f(x) is shifted 3 units…

A: Given that y=f(x)minimum point on the graph is (2, -1)

Q: Find the positive critical point of the function f (x) = x / x^4 + 4

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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: Find the point on the graph of the line f(x)=3x+4 that is closest to the point (6,3) x= y=

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Q: 1.Discuss two practical applications in which “piecewise functions” are used either explicitly or…

A: We will answer the first three questions. Please resubmit the other question as a separate one.

Q: Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y =…

A: Given,     f(x)=x3+g(x)

Q: dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?

A: Solution

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 &amp; the line tangent to y=gx at x=5 is y=6x-27. Put x=3…

Q: An animal feed company must produce 200 kg of mixture consisting of ingredients x and x2.x costs 3…

A: we will first formulate the LPP using the given statements and then we will find the optimal…

Q: Find the local maximum and minimum values and saddle point(s) of the function x² y² – 8x + y f(х, у)…

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Q: 10. If the minimum of the function y =x 2 –4x+21 occurs at x =2, what are the coordinates of the…

A: In the question , it is already given that minimum is occurring at x = 2 So, just put the value x =…

Q: Find the critical points of the function f(x)=x2−4x+3x−2.

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Q: 4. a) Find the value of x where the function f(x) = (x – 4)3 is not differentiable.

A: According to power rule of differentiation , .

Q: I want solve it in а раper 3- Show that the function y = x³ + 3x + 3 satisfy the y= + xy - 2y = 0

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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: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: 3 The graph of f(x) = 2x° + 15x² – 84x + 24 has two horizontal tangents. One occurs at a negative…

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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.

Q: 9. Find the family of the curve whose slope at any point is √x + √x and also the member which passes…

A: According to the company rule we can answer only first question and rest can be reposted.

Q: 7. a) Determine the restrictions on the y- intercept so that y = 3x2 + 6x - 1 intersects with a line…

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