Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) f(x) = x² – 6x

Q: Let f (x) = x3 – 3x2 – 1, x 2 2. Find the value of df-1 at the point x = -1 = f (3). dx -

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Q: f (x) = x³ – 3x %3D 34 - the distance between the local extreme points of the function OA) V5 B) 2…

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Q: 2. F(X) = x (x-6. %3D

A: Find the critical numbers of F(x) using first derivative

Q: find the diferential of the function when x = 2 and dx = 0.1 f(x) = x ln (x^3 + 2x - 4)

A: We will use the definition of differential.

Q: B-Test and proof the function So(x In x)? dx

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Q: The function f whose tangent has slope x3. +2 for each value of x and whose graph passes through the…

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Q: Find the value c in the interval [0,1] where f'(c) = f(b)-f(a)/b-a f(x) = 1/(x+1); [0,1]

A: Given,           fx=1x+1 ;  0,1

Q: Find all maxima and minima for the function f(x,y) = - 7x - 2xy -8y +64x- 38y+ 2. EI ly vl ond f y…

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Q: Find the absolute extremum values of f(x) = xe² xez-2x² 3 on the interval [0, 1]. (Note: ez ≈ 0.22)

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Q: Find, if they exist, the extrema of the function: f(x, y) = x² + 3y? + 4,

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Q: Find f'(x). f(x) = 2x° - 6 ex f'(x) = (Type an exact answer in terms of e.)

A: We have to find

Q: Let f(x) = e3x-5 a. Find an expression for dy. b. Estimate dy for x = 2 and dx 0.04

A: To find an expression for dy Also to find the value of dy at x=2 and dx=0.04

Q: Find the value of b such that f(x) = Vx + 1+2 has inflection point at x = 3.

A: Solve the value of b

Q: f(x) = 5 S 2+3x² + 2x_r +1 x = 1 Determine the type of discontinuity of the function at x=1. 2.

A:

Q: Consider the function f(x)=12x^5+75x^4−120x^3+3 f(x) has inflection points at (reading from left to…

A: For finding inflection point , f''(x) =0 .( find 'x' )

Q: On what interval(s) is the function y = –2x² + 3x/3 both increasing and concave down?

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Q: If f is an even function, why is S", f(x) dx = 2 f“ f(x) dx?

A: A function is said to be even if f-x=fx   We have to prove  ∫-aafx dx=2∫0afx dx   Consider left hand…

Q: The domain of the function f(x)= tanh( - 23) is (A, 264)

A: Given,          The domain of the function fx=tanh-1xk-23 is A,264.

Q: f(x + h) - f(x) otient, for the function f(x) = x, and si

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Q: For f(x, y) = xex2y, find fx and fy, and evaluate each at the point (1, ln 2).

A: Given: fx,y=xex2y

Q: Please show step-by-step solution!

A: According to chain rule the derivative of the f(g(x)) is [f(g(x))]’=f’(g(x)) * g’(x)

Q: Find the local extrema of the function f(x)=x2e−x.

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Q: For function f(x,y) to have no extremum value at (a,b) is? 1) rt - s>0 2) rt – s?<0 3) rt - s? = 0…

A: To select: The condition for the function f(x, y) to have no extreme value at (a, b).

Q: For the function f(x)=e5x+e−x defined on the interval(−∞,1], find all intervals where the function…

A: Find all the intervals for where the function is increasing and decreasing

Q: For what value of x does the function g(x) =--x³ + 2x? strictly concave downward? А. x> 2 В. х>1 С.…

A: Use the property of strictly concave downward i.e.g"(x) &lt;0.

Q: If f(1) = 12, f' is continuous, and f'(x) dx = 17, what is the value of f(4)?

A: topic - definite integration

Q: If f is an odd function, why is S, f(x) dx = 0?

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Q: If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

A: f is a positive function and f''(x)&lt;0 for a≤x≤b This tells us that f is concave down over the…

Q: Two runners start a race at the same time and finish in a tie after 5 minutes. Prove that at some…

A: Suppose gt and  ht be the positions of the first and second runners at the time t respectively.…

Q: The value of b for which the function f (x) = sin x- bx + c is decreasing for x E R is given by (a)…

A: Given function is f(x)=sinx-bx+c differentiating with respect to x we have, f'(x)=ddx(sinx-bx+c)…

Q: Find the local extreme values of f(x, y) = 3y² – 2y³ – 3x² +6xy

A: According to Second Derivative Test for Local Extreme Values Suppose that f(x,y) and its first…

Q: Differentiate the function. y = In(12 + t – t31)

A: We have to find derivative

Q: Find the inflection point(s), if any, of the function. (If an answer does not exist, enter DNE.)…

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Q: (b) If 38 10z f (2) = (2** + 6) e then at how many points the function f (z) is not differentiable?

A: f is every where differentiable, there are no points such that the function f(z) is not…

Q: Let f(x) = x² – 4x – 5, x > 2. Find the value of df-1/dx at the point x = 0 = f(5).

A: (f-1(x))' = df-1dx = 1f'(f-1(x))

Q: For what values of a, does the function z = x°e¯i satisfy the equation Y Zyy = Zx – Zy ?

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Q: find the diferential of the function when x = 2 and dx = 0.1 f(x) = 3 / (x-1) ^ 2

A: Given that f(x)=3(x-1)2 Take the derivative with respect to x, dfdx=-6(x-1)3df=-6dx(x-1)3

Q: If f(1) = 13, f' is continuous, and F'(x) dx = 18, what is the value of f(6)?

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Q: 2. a) Find a formula for f1 for the function y = f(x) = vx – 35

A: To find f-1 for y=f(x)=√(x-35)

Q: Consider the function f (x) = 2 sin a + 3. Which graph represents the solution set of f (x)? 2m 3n2…

A: Consider the function  f(x)=2sinx+3

Q: Find the critical point of the function f(x, y) = – 7 – 5x + 4x? + 6y – 2y? This critical point is…

A: f(x,y)=-7-5x+4x2+6y-2y2

Q: f(x) = In(x² + 1)

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Q: For the function f(z) = ¹, the point z 1-e Z = 0 is

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Q: Find the absolute extrema of fGx\=x. %½x°- 2 x+1 on the interval E1,2I.

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Q: (x) is an even function, and if f 6 f(x) dx = 15, find f³, f(x) dx.

A: Given query is to find the value of the Indicated integral.

Q: The antiderivative of the function f(x) = .3+9x is

A: find the anti derivative (integral) of fx=56 .3+9x3

Q: Q4) f(x, y) = x'/3 – x/ay² is harmonic ? Does the function

A: our objective is to conclude result.

Q: let f(x)=5x^3-9x^2-3,x ≥ 1.5. Find the value of (df^-1)/(dx) at the point x=f1 =f(3)

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.