15. The range of values ofx for which the function f:x+x² – 6x + 4 is increasing is A x>3 B x<3 C -3 3

Q: 1. Find the local extrema of f(x) = x* – 2r2 +1, and state the intervals on which this function is…

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Q: 1 1 suppose / f (x) dæ = –2 and / g (x) dæ = 1. What is the 1 value of / (f (x) + 3g (x) – 2) dæ?

A: Given : ∫01fxdx = -2∫01gxdx = 1

Q: #2 Given: F(x) = 2x 2+ 1, G(x) = 2x - 1, H(x) = x F(-2) = 9 -7 17

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Q: 4. Given that (fog)(x)3= 4. and f(x) = Sx+4 9x-2 Determine g(x). Hence, find g(0)

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Q: 2 6wen that f(x).(32-5 find the solution set of a for (1)decreasing Which the function is…

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

Q: 2. Evaluate the piecewise function at the given values of the independent variable. 4x +4 if x < 0…

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Q: 1) Find all relative extrema in the function f (x) = x 3 + 3x2 – 24x + 12.

A: For relative extrema the derivative of the function will be zero. Thus,…

Q: 1. What are the x-intercepts for the function f(x) = x2 + 2x – 15? А. (0, -5), (0, 3) В. (0, 5), (0,…

A: Given, f(x) = x2 + 2x -15

Q: 1.4 For which values of a ER is the function f(x+ iy) = (a²x – axy) + i ax? + ay an entire function?

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Q: 1) Find all relative extrema in the function f (x) = x³ + 3x2 – 24x + 12. 2) Find all points of…

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Q: 3. Use the graph of y = f(x) to graph y = -f(x – 4) – 1. 3 y = f(x) -5-4-32-1 1 2 3 4 4. Determine…

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Q: Find the absolute extrema of the function f(x)= (x^3)-(9/2)(x^2)-30x+3 on the interval [0,6]

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Q: 18) Match the graph with the correct function. (a) f(x) = -3 + In x (b) f(x) = 3 + In x (c) f(t) =…

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Q: 1 b) x 2. If f(x)=x(2 In x-3) Find f'(x) 24/mx-4x

A: #2 Given, f(x)=x22 ln x-3

Q: 1. Solve the following problem. What value of k makes the function continuous at x = 3? x2 + 2x - 3…

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Q: 2 If f(x) = and g(x) then (g of)(x) is equal to x + 3 1 + 3x A x + 3 D 2x x + 3 2х 1 + 3x 2x

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Q: 17. Given the function f (x) = x2 + 2. Find and simplify the difference quotient. S(x+h)-f(x) h 0

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

Q: 10. What value of k makes the function {2x - (4(x + k) if x > 2 if x <2 f(x) continuous at x = 2? А.…

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Q: 5. Determine the values of x for which the function is continuous. 3r +1 e. f(x)= /x – 3 2- 8 4x d.…

A: The function √(x-a) is continuous iff x&gt;=a The function 1/(x-a) is continuous iff x≠a

Q: 3. Determine the values of a and b if the given function f(x) is continuous. (2x + 6 ,x 2 Solution:

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Q: 2. Find the x-coordinate of the point(s) of discontinuity of the following functions -16 x3 16х — 4,…

A: For x&lt; 3 , f(x)= -16 is continuousFor 3&lt;x&lt;6 , f(x)=16x-4 is continuous tooFor x&gt;6 ,…

Q: (i) Discuss the continuity of the function f(x)={x2−3x if x&lt;22x+4 if x≥2 on the open interval…

A: Part (i):   In the region x &lt; 2 the function is defined as x2 – 3x. This polynomial is continuous…

Q: 1. Suppose: f(x) = 2x + 5, g(x) = - x². a. Find g 8(S(x)) 'b. Is g(f(x)) one to one? Justify your…

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Q: For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x 3 с 3

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Q: 7. The critical points of the function f(x) = 1³-272 are (a) ±3 (b) ±1 (c) +√2 (d) 1

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

Q: Consider the following function. x2 + 2x + 2 2 x3 3 (a) Find y' = f '(x). f'(x) = (b) Find the…

A: Given: - The function is, y=x33+x22-2x+2 To find: - (a) The derivative of the given function. (b)…

Q: (i) Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the open…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: 2] 20 Determine which value(s) are excluded from the domain and range of f(x): 4+x %3D X-3 Excluded…

A: fx=4+xx-3

Q: 11. Decide algebraically if the functions given below are even, odd, or neither. a) f(x) = -7x - 3x3…

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Q: 5. Find the x-coordinates for all points of discontinuity for f(x)- 「X316, xśl x〉 1 2 c. 1, 32d.…

A: First we check the limits as x approaches to 1 from left side and right side .

Q: 4) Find the value of the function f (x) given in the table below at the point x = 3 by Aitken…

A: Aitken method is used to find out the interpolation value of the function f(x) at a particular x…

Q: 11. Given that f (x) = 2x +1 and g(x) = x² find (a) (fog)(2) (b) (go f)(x) (c) f(f(x)) (d) g(g(3))

A: we have to find the following

Q: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

Q: 4. F(x)- F(x)=L x-1 5. Gx)-8-2x 6. h(t)= 2-1

A: For a real valued function f(x) We have to find all points x where f(x) is well defined Those points…

Q: х2 — 4 3. Do you agree with the contention that the functions f(x) = x + 2 and g(x) х — 2 are the…

A: f(x)=x+2 gx=x2-4x-2=x-2x+2x-2=&gt;gx=x+2

Q: 1 For what value of x does the function f(x) = -x 4x attain the absolute maximum in the interval…

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Q: 11. Use the given graphs of f and g to evaluate (5f(x)+3g(x)) dx |x=4 5- y = f(x)/ -4- y = g(x).- 2-…

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Q: 4) Determine the critical values of each function. 4x a) f(x) =7+1

A: 4a) The given expression fx=4xx2+1 Differentiate with respect to x f'x=4x2+1-4x2xx2+12f'x=4-4x2x2+12

Q: 1 For what value of x does the function f(x) = =x³ – 4x attain the absolute maximum - in the…

A: here option (c) is true on doing differentiation we get the  f'(x)=3x^2/3-4 f'(x) =x^2-4 put f'(x)…

Q: 6 — 2х if x x2 – 16 For which x E R is f(x) continuous? You must give j your answer.

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Q: 2. Find the value of k so that the function defined by f(x) Sx² + 20 x 5 continuous at x = = 5.

A: We know that, a function fx is said to be continuous at x=a if and only if Left hand limit=Value of…

Q: 2. If f: R→→ R satisfies f(1) = 3 and f'(x) ≥2 for all x's, how small can f(7) be?

A: Here we have to find the smallest value of f(7).

Q: Where is the function undefined and where is it equal to 0. f(x)=3e^2x-3

A: We can solve above question both through algebra and also through drawing it's graph. Both of them…

Q: Find the critical point for the function f(x)=5x2. 4 - 1 40 none O 18 O 4

A: Given function is                                                f(x)=5x2-x4 we have to find…

Q: The critical points of the function f(x) = 2x – 4x +7 is a) 1 b) 0 c) - 1 d) None of these

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Q: 9. Which function is greatest at x = 4 O A. f(x)= 3* O B. f(x)= 3(x) O C. (x) = x3 O D. none of the…

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Q: (Bx2 – 3 Bx +2 if Suppose that f(x) = x< 2 if Find the value of ß so that f(x) is continuous…

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Q: 4- Legendre function of P4(x) equal to : a) P,(x) = (35x* – 30x? + 3) b) P, (x) =(35x* – 30x? + 3)…

A: Given:        The Legendre Equation is given as                1-x2d2ydx2-2xdydx+nn+1y=0 The…

Q: Find the absolute extreme values of the function on the 11) F(x) = 0.5 s x s 2 x2

A: We first find the critical values by solving F'(x)=0 F(x)=-2x2F(x)=-2x-2F'(x)=-2(-2)x-3F'(x)=4x3For…

Q: 6) Suppose that f(x) = x2 + 2 for -2 s x S 2. The range of the function is : a) O {y : 2 < y < 6}…

A: Given            f(x)=x2+2

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.