2. Evaluate the piecewise function at the given values of the independent variable. 4x +4 if x < 0 f(x) = %3D x+7 if x20 (a) f( – 4) (b) f(0) (c) f(1)

Q: Find the critical points of the given function. 1 a) f(x) = -√24/3+2¹/ +2-2/3

A: Since multiple questions are asked, I am answering first question

Q: Find the value of the constant k that makes the function continuous.

A: A function is relation between set of inputs and output. The piece-wise function is a function which…

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

A: to find the value of fx given in the table at the point x=3 by Aitken method  solution we will solve…

Q: Suppose that f is a linear function with slope -3.4 and that f (3) = 4. What value of x gives f(x) =…

A:

Q: x2-8 If fx)= X-4 where is f not differentiable?

A: Given the function

Q: Increasing and decreasing functions Find the intervals onwhich f is increasing and decreasing.…

A: Given: fx=4-x2, fx=x2-16, fx=x-12 We know that any given functionfx is increasing in a interval if…

Q: he average cost function is defined in economics as C¯(x)=C(x)x, where C is the cost of…

A: Given:  C(x)=0.01x3−0.4x2+13x+400,

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: 2 The function f(x) is linear and it decreases for all values of x. On the coordinate plane, draw a…

A: We want to find a decreasing linear function.

Q: 8 Where does the graph of the function hx) = x*+3x-4 cross the x-axis? A. x= - 2 and x 2 B. x= - 2,…

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Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

A:

Q: 2. Consider the following function: y = f(x) = x" – 14x® (a) Determine in which regions this…

A: A function is increasing or decreasing that is determine by    f'(x)&gt;0 or f'(x)&lt;0 A function…

Q: 2. Evaluate whether the following initial values is true in the function: y = 4cos-+ e-2x 2.a) 2.b)…

A: Given , y=4 cosx2+e-2x

Q: 5. The coordinates of the hole for the function f (x) x²-4 are: x-2

A: Given function, f(x)=x2-4x-2

Q: Show your step-by-step solution. Find all the relative extrema and saddle points, if any, of the…

A: To find out the relative extrema and saddle points.

Q: x2 – 4 3. Do you agree with the contention that the functions f(x) = x + 2 and g(x) х — 2 are the…

A:

Q: 21. Suppose f(x) = A and g(x) = v2*. Find the x-value for which the two functions are equal.

A:

Q: 1 For what value of x does the function g(x) 2x concave downward? А. x 2 -1 В. x2 0 С. x -2 x 2 D.

A: Given:    gx=13x3-2x2 The first derivative of function g'x=ddxx33-2x2…

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

A:

Q: 5. Consider the function (x2 + y²)e-¯-. Provide the number of maxima of f(x, y). In case there is no…

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Q: 2x + 5; if x 3 Find the value of functionf at x = 3.

A: Topic = Function

Q: For what value of X does the function f(x) = x³ – 9x² – 120x+6 have a relative minimum? A 10 В) 4 3

A: f(x)=x3-9x2-120x+6

Q: #2. Determine the equation for piecewise function f(x) given its graph below. -9-8-7-6-5-4-3 f(x) 5…

A: Given data:-

Q: 2. f(x)=x²-6x X -6x Vertex x-intercept(s)

A:

Q: For what value of X does the function f(x) = x³ - 9x² – 120x+6 have a relative minimum? А) 10 В) 4 D…

A:

Q: 5. Find all relative maxima of the given function. y =x* -8x' +16x² +3

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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

A:

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: . If x is large, which function grows faster, f1x2  2xorg1x2  x2?

A: To determine for the large values of x, which of the functions f(x)=2x and  g(x)=x2 grows faster.

Q: evaluate h(x) = 2x-1/ 3x+1 at the given value of x h(s-5)= ?

A:

Q: For what value of X does the function f(x) = x³ – 9x² – 120x+6 have a relative minimum? (A) 10 (в) 4

A: solution is given below .

Q: 21. Suppose f(x) = G and g(x) = v2**. Find the x-value for which the two functions are equal.

A:

Q: 10. Find y' with the implicit function below. 3(x² + y²)² = 100(x² – y²)

A:

Q: 12. If f(x) is a non-constant linear fucntion and g(x) is a quadratic function, then what type of…

A: f(x) is linear function so f(x) can be expressed as  f(x)=ax+b, where a≠0 and b are constants. g(x)…

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: What is the value for k if f(x) =x² + kr + 13 is an even function?

A:

Q: 4. The function f(x) = x³ – 6x² + 9x – 4 has a relative maximum at (A) x = 0 (B) x = 1 (C) x = 2 (D)…

A: Let f(x) = x3 - 6x2 + 9x - 4 Suppose the function has critical point at x = c then If f'(x) &gt; 0…

Q: 2 The critical point for the function g(x)= X +4x is Select one: a. (4,-2) b. (-2,4) C. (2,4) d.…

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Q: f(c) {}} [=+3 = < (3x + 1

A:

Q: x2 – 4 3. Do you agree with the contention that the functions f(x) = x+ 2 and g(x) х— 2 are the same…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

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

A: To find the range of x for which the given function f(x) is increasing

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: Compute f(x)dx 2x if x <1 4 if x21 f(x) =

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Q: A function has f''(x) = 10 and has f'(4) = 0 and f(2) = 4. Find f(x).

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Q: 5 If f(x)=g(x)+3 where 2<xs 5, then [[{(x)+g(x)]dx = 2ſ8(x)+3.

A:

Q: 3. Do you agree with the contention that the functions f(x) = x+2 and g(x) x-2 are the same in every…

A:

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: Q 2/ find the value of (k) to continue the function Vx+1-/2x x + 1 f(x)= (k x2-x X = 1.

A: The detailed solution is as follows below:

Q: 3. Find the value of the constant k that makes the function continuous f(x) = {x² – 6, x + 4k, x 6

A:

Q: 1 You are given the function f(x) = x2+7 f(x) is concave up whenever:

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!