The function f (x) = x' + 1 is continuous in the interval [-,2, 4] and differentiable in the interval (-2, 4). The value of the constant c, S(4)-/(-2) -2

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: find the critical points and apply the Second Derivative Test (or state that it fails). f (x) = sin2…

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: Find the first derivative: y= ln v5x3 –- 2 5, O y = 222 %3D 523-2 O y' = 322 5z3-2 O y' = 622 5z3-2…

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local…

A: Given:   f(x) = x2 To determine whether f(x) has a local maximum or local minimum at the critical…

Q: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

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Q: Find the derivative of Ox²2cosx + 2xsin x O 2xcos x O x² sin x + 2xcos x O x2cosx y=x²sinx

A: We know that if f(x)=g(x)h(x) then  f'(x)=g'(x)h(x)+g(x)h'(x)

Q: The normal line to the curve y = -2x2 at a point in the fourth quadrant passes through the point…

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Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

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Q: The second derivative test fails when f" is zero or does not exist at the critical number of the…

A: Given data: The value of the second derivative of the function is f''=0.  Suppose at the given point…

Q: The first derivative of y=cos(tan(x2-7x+1)) is... Turunan pertama dari fungsi y=cos(tan(x2-7x+1))…

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: 9 Derivative of fi») 1x 4 . 5. 1 f) 1x1cosx, fird f'n)

A:

Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

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Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

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Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

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Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: Find y''by implicit differentiation. 2x3 + 5y3 = 2

A: We can find y" using implicit differentiation as below.

Q: Suppose that a drug is administered to a person in a single dose, and assume that the drug does not…

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Q: Find the partial derivative. 4 = (x² + 6x – 3y)* - dz

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Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

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Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

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Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

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Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

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Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

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Q: If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f…

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Q: Find the orthogonal trajectories of family of curves y = ax5 (SOLVE BY USING DIFFERENTIAL…

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Q: Determine the n-th derivative fn) of the function f: (0, +0) → R, f(x) = x ' exp ( 1 - ), n EN

A: f(x)=1x,  f:(0, +∞)→R,…

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

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Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.