(i) Interpolate the missing entries | 0 | 1 | 2| 3 | 4 | 5 y= f(x) | 0 | – 8 15 35

Q: A) f(-1)-f(-2) (-1)-(-2) QIn parts (A)-(C), find the indicated quantity for y=f(x)=4-x². = N

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Q: (d) (x– 2)* + (y-9)* =1 (e) x² + y² = 1 (f) x² +(y+5)° = = 25

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Q: +2メ+2 2=f(x.y)-4xy 3. +2メ+2y2= T %3=

A: Derivative: - The function's derivative is the equation we discovered. The derivative is defined as…

Q: 3 – x2, 0<x < 1 | f(2) dr, where f(x) = 1<r< 2.

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Q: ) = x² + y² - 8x - 6y subject to the

A: Given that fx,y=x2+y2-8x-6y. First we have to find the extreme point on the domain given in the…

Q: f(x) y = g(x) %3D -5-4-3/2-1 1 2 3 4 5 -4 3 10

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Q: c) f(x) = 3x – 2 5 3メー2 51

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Q: #20

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Q: 5. State the equation of f(x) if D = {xER\x - and the y-intercept is (0, ;) 2x+1 x+1 f(x) : f(x) а.…

A: Equation of the function

Q: If f(x, y) = 2x+6 (2a-6y) of then is given by:

A: In the above question we will take y as constant since we have to partially differentiate it with…

Q: Find the Critical Numbers of the Function: f(x) (x2 + 6x - 7)2

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Q: -Зx2-5х+2 -19x-24 38х-4 3. f(x) = (Hint: f'(x) = and f"(x): (x+4)3 (x+4)2 )Find x and y intercepts…

A: Given the function

Q: 2. -1 2 f(x) -5 1 3 1 -5 A. y = 3x2 -x + 1 B. y = -3x? + x +1 C. y = 3x² + x -1 D. y = -3x + x – 1

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: If f(2) = 15 and f (x) > 2 for 2 s x s 4, how small can f(4) possibly be?

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Q: a) -x +y - z = 0 2y + z = 3 z = 0

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: c) f(x) = 2* + 2 for all x e R

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Q: 6. f(x) = x + ty -41 -4-2 0 2.

A: Solution: The objective is to graph the given linear function

Q: [5 < x < 8} 15<y<8S° f(x, y) = x² – 12x + y² – 8y on -

A: Given on . For global maxima and minima find the value of in given square region.

Q: y = x²-1, stretched vertically by a factor of 3 is a) y = f(x) (b) y = (C) y = f(3x) (d) y = f(x) +…

A: Given,           The function is y=x2-1.

Q: Ex 2. Find the critical points for: |a) f(x)= 2x³ +3x? b) f(x) ={Vx² –1

A: Critical points are the points where local maxima or minima of a function occurs.

Q: 3.) Give the coordinates of any points of inflection. f(x) = x³ + x² – x +1

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Q: 2. Given : f(x) = {x² - 3, x+3 6, %3D X = 3

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Q: а. (k — h)(1) b. O(1) 4+ y= h(x) 1+ + 2 + + 6 c. (h o k) (0) -6 -5 -4 -3/-2 -1 4 y = k(x) d. (k o…

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Q: b) f(x) = V3 + x² at x = -1

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Q: f(x)=1/5 x^5 - 8/3 x^3 +16x what are the critical points?

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Q: x³dx √1+x² (A) / (1+x³)³/² + (C) &n[√x - √₁ + x² + c 31. If I = f- then I equals to - " (1+x³) ³/²…

A: Follow the procedure given below.

Q: If f(x) = x³ – 2.x² +3 , the only point where f could change the concavity is 2 b) x =- 3 a) x =- c)…

A: Finding the inflection points

Q: Discuss the continuity of the function on the closed interval.

A: Given, f(x)=x, x&lt;12,x=12x-1,x&gt;1

Q: e) xy+ y² = 1 f) x2/3 + y y²/3 = 1 g) x3 + y4 = 16

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Q: 3 2 y X-3x-x t3 From X = -1 to X= 8

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Q: f (z) 10x +3 (2)) g (x) = -7x- 4 %3D What does (f-g) (r) e

A: To solve this question, We will use - (f-g)(x) = f(x)-g(x).

Q: f(x) = g(x) + h(x), where g(x) = 2x 4 + 12x2 + 4 and h(x) = -5x 3 - 3x

A: Given gx=2x4+12x2+4hx=-5x3-3x fx=gx+hx

Q: a) Suppose that f(3) = 15, f'(3) – 5 and let H(x) = Vf(x)+ 10. Find H'(3). b) Let f(x) = cx +…

A: (a) Differentiate the function Hx with respect to x to find H'x.

Q: 2) f(x) =15 - 8x A) s'(s) = B) s"(x) = x 2 C) 3x- 15 s"(x) = 8. D) s (x) = x - 5 3.

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Q: _1. f(x) = 2x3 2. f(x) = 2* 3. y = e* |3|

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Q.No.4 Differentiate the following Y= (x²+3)x' Y= ax²+b/ cx Y= 7x*+2x³-3x+37

A: I have differentiate all three functions with respect to x

Q: the extreme points of f(x,y) = 3x²y+y3-3x² - 3y² + 2.

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Q: (x2, f(x) = { ax + b, 3 s x s 4 [x+12, х>4 x<3

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Q: -8 f(1) – 4 g(4) =[ %3D 8- 6+ y= f(x) 2+ -8 -6-4 6. -4+ y=g(x) -6+ -8- ఈ

A: Given, The graph of the functions  y=fx   and  y=gx We have to find the value of expression…

Q: f(x) = -0.1x4 - 0.15x3 - 0.5x2 - 0.25x + 1.2 at x = 0.5 using: first backward difference with…

A: f(x) = -0.1x4 - 0.15x3 - 0.5x2 - 0.25x + 1.2at x = 0.5 using: first backward difference with…

Q: The Range of y = [2x + 1] is Z. FO * 2.2 2х-1 If y = Vx? – x then y' 3. 3 Vx2-x F O

A: Given(1)-      y=[2x+1]As we know that is set of all valid output values or all valid y values…

Q: (14) f (x,y)=e" (x² +y²)

A: f(x,y) = (x^2+y^2)e^-y fx= 2xe^-y fy= -(e^-y)(x^2+y^2)+ 2ye^-y fxx = 2e^-y fyy = (e^-y)(x^2+y^2)…

Q: Find the value of x and y for f(x)=3x2+9xy-y2-9x,if fx(x,y)=0 and fy(x,y)=0

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Q: What is the value of f(1) - 16B in I x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 2 0

A: Given; ∫x3lnxdx=fx14lnx-B+C    ...(1)   First, we have to find the integral value. I=∫x3lnxdx Apply…

Q: E f Cx) = x+ X -3x-3:0 Two decimed.

A: x^3+x^2-3x-3=0 (x³+x²)-3x-3=0 x²(x+1)-3(x+1)=0 (x²-3)(x+1)=0 Equate  (x²-3)=0 Using identity…

Q: The domain of y = 5f(2x +4)+3, where f(x)= - is Select one: O a. x*0 O b. x* - 4 O c. X# - 2 O d. x*…

A: We need to find the domain of y=5 f(2 x+4)+3 where f(x)=1/ x

Q: b) f(x) = v3+ x² at x = -1

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Q: If f(x) = 4 – x² & g(x) = vx then find (fog)(x) » (gof)( x + 8 If f(x) = 3x – 8 & g(x) = then find…

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Q: The function f: R R satisfies the condition mf (x-1)+nf(-x) =21x|+ 1. If f(-2) = 5 and f(1) = 1,…

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Q: 7 If f(x, y) = (3x³ + 2y² – 30)', then fy is - given by :

A:

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.