1. Find the relative maxima and minima of y by the second-derivative test: (a) y = --2x? + 8x + 25 (b) y = x³ + 6x² + 9 (c) y = }x³ – 3x² + 5x + 3 (d) Y = 1- 2x 2x (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: find the orthogonal trajectories of the family of curves x2+y2=a2

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Q: Find the orthogonal trajectories for the family of curves 6x² + y² -9ax=0.

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Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: Find out all the relative minimum and maximum values, and saddle points of the function h defined by…

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Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

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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: Find all points (x, y) on the graph of ƒ(x) = 3x2 - 4x with tangent lines parallel to the line y =…

A: Since the tangent is parallel to y = 8x + 5. Hence, the slope of the tangent = slope of the line = 8

Q: If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies…

A: It is given fx=x4, gx=x3, f'(x)=4x3 and g'(x)=3x2.

Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: If the utility depends only on the consumption of x and u (x) = ( 2a¯i + 3) (-4xi +2), is Marginal…

A: Given u(x) = 2x-12 + 3-4x14 + 2

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

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Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

A:

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Maximize f=-x-3y subject to -2x+y = 2 X,y >= 0

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Q: y = x3 + 1,

A: We have to find

Q: Identify all local extrema and saddle points of f(x.y) = 80x + 80y - x - y %3|

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Q: 4. Find the slope of the line tangent to the graph of 1 f (x) = 2x4 – 32x3 + 17x2 – 9x + 4 at x 2 -…

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Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

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

A:

Q: 3. Find the fixed point(s) of f: [1, ∞)→→ [2, ∞) defined by f(x) = √²+x.

A: 3) To find: fixed points of f:[1,∞)→[2,∞) defined as f(x)=x2+x.

Q: y = 3 – 2x + x?

A: In this question, we need to find the critical points and test for maxima/minima of y=3-2x+x2.

Q: 2) Find all relative extrema of ƒ(x)= x* – 4x³

A: Answer

Q: Find the critical points of y= -2x^2 +4x +3 and apply the Second Derivative Test to find the maximum…

A: Critical point and extreme points

Q: 8. Find the extremum and saddle points of the function f(x, y) = x³ – 3ry + y³ if any

A: Given function is fx,y=x3-3xy+y3

Q: Determine the critical points of the curve y = x³ – 5x2 - 36 x + 25.

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Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: 3. Find the slope of the line tangent to f(x) = In(4x² – 3) at (1,1).

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Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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Q: 3. Find the critical points of the function f(x, y) = 4x2 + 9y2 + 8x-36y + 24 and use the second…

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Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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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: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

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Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

A:

Q: 2. What is the slope of the normal line to the curve 4x2 - 9y2 = 1 at point (3,2) ? a. 3 b. - 8. С.…

A: Normal at any point on the curve is a straight line that intersects the curve at that point and is…

Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Determine all the critical points for the function y = Vx² (2t- 1)

A: Given function is in two variables x and t For critical points we calculate Partial derivatives…

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: 8. Find the local maximum and minimum values and saddle points of the function f(x,y)=2x + 4y +3x²…

A: This is a problem related to maxima and minima. Please follow the procedure given below.

Q: Find the critical points of the function f(x) = 4x° – 12x.

A: The given function is fx=4x3-12x. The critical points of any function is given by f'x=0.

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: determine the coefficients of the equation y=ax^3+bx^2+cx+d so that will have a slope of 9 at…

A: The equation y=ax3+bx2+cx+d so that will have a slope of 9 at (-1,-4),a critical point at x=2, and a…

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: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: find the marginal revenue of the function. Using the quotient rule.  40x^2 -20x/x^2-10-2

A: Given: Revenue FunctionRx=40x2-20xx2-10-2 To Find: Marginal Revenue Concept: a. Marginal RevenueMx…

Q: 2. Estimate the slope of ffx) at the point: a) where x = 3 b) where x = 2 f(x) 4 2 1 2 3 4 5 6 3. 1.

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Q: If f(x)=x* and g(x)= x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule multiplies derivatives to…

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Q: Find the critical points/max/mins: Of the curve: y=2xln(x)-x2

A: I am attaching image so that you understand each and every step.

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.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.