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

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: (2x+1 x² +2 x> h) Xsh Q3) If the function f(x) %3D having limit at x h. Find the value of h.

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Q: 2. Find and classify the critical points of the function f (x, y) = 6x2 – 2x³ + 3y? + 6xy

A: The solution is given below in the next step:

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: suppose f is a continuously differentiable function satisfying f(3)=6, and f'(3)=5. Find (f^-1)'(6)

A: Given f(3)=6, f'(3)=5  To find f-1'6 By the formula, f-1'x=1f'f-1x And we know that if f(a)=b then…

Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: 21) Find the maximum and/or minimum values of f (x, y) = x² + 2xy + 2y² - 6y + 2

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Q: Find all the critical points of the function 1 3 f(x,y) = x° -6y-7x+18y-3 What are the critical…

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: 4. Find and classify the critical points of each of the function f(x,y) = x² + y² + 3xy.

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Q: 22--15 if r#3 Find the value of the constant k that 5. f(x) = makes the function f(x) continuous.…

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Q: 3.fCx)3D63X²4X+2 x<1 2x-1 X71 Part A: IS f(X) lontinuous ar X-1? JustfY answer. Palt…

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Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: Q.3/ Find and classifies the critical point of the following function: F(xy)=-x - y + 2x+ 2y +2 (x2…

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Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

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Q: 1 For a function f(x), we have f(x) = 1+ x? and f(0) = 0 prove that x +y f(x) +f(y) =f 1-xy

A: We will prove as following.

Q: 1. Find the critical numbers of the following function. f(x) = x-v*(x – 2)

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: 12. Consider the function f(xx) = 2x² + y* + 4xy. %3D (a) Find the critical points for this…

A: Find the critical points of the function fx,y=2x2+y4+4xy

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

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Q: Q.3/Find and classifies the critical point of the following function: F(xy)=-x-y + 2x+ 2y +2 (x2 0,…

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Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: '12 9. If f is continuous and f(x) dx = 20, find f(2x) dx.

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Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

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Q: 1. Find and classify all critical points of the following function: f(x, y) = x* + 2y² – 4ry

A: Given the function

Q: -1.5 0 1.5 For what value of constant c is the function k(x) continuous at x = 0 if k(x)= No such…

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Q: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

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

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Q: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

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Q: If f(x) is a twice differentiable function with •1 f(0) = 5, f(1) = 4, f'(1) = 2, Then So 2x f"…

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Q: the critical points of f (x) are x = -2 and x = 1, and f '(0) = -6 we can conclude that in the…

A: Solve the following

Q: Consider the function f(x, y) = e-xy It is possible to state that f reaches global extremes (global…

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Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 4 If the critical number of the function f(x) =x is x 0, then the function %D is decreasing on (0,0)

A: We can find the decreasing interval as below.

Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

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Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

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Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: In Problem (A), Show that f(x, y) is differentiable at the indicated point. A) f (x, y) = (x2 +…

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Q: 3. Find constants A and B such that the function x2 f(x) = if x 2 is differentiable at x = 2.

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Q: 2 2 If f is continuous on [0, 2] and / f(x) dx = 5, find the value of | f(x – 2) dæ.

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Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: 1)Classify the critical points of the function f(x,y)=x²+y³+x²y+4

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Q: The function if x 1 has critical points at... (Choose all that apply.) x = 0 x = -1 x = 3

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