Show that x – P VB + (d - x)* g(x) is a decreasing function of x.

Q: The function given by f(x) = -3x + V2x + -x (is/is not) a polynomial function.

A: A polynomial is a function such as quadratic, cubic and so on which involve only non-negative…

Q: 6. Eliminate the arbitrary constants from the relation y=ax² +bx +c.

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Q: Find the maximum and minimum value of f(x,y) =x3+3xy2-3x2-3y2+4

A: fx,y=x3+3xy2-3x2-3y2+4   fx=3x2+3y2-6x   fxx=6x-6   fxy=6y   fy=6xy-6y   fyy=6x-6

Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

Q: 9. Let f(x) = xr – 3x² + 3.

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Q: 3. Find f'(x) for f(x) = v5 + e2x xe2x-1 А. V5+e2x 1 2v2e2x С. 5+ e2x e2x D. V5+e2x V5+e2x B.

A: In this question, concept of chain differentiation is used in this question.

Q: p (x) = xª – 8x3 + 14a² + 8x – 15

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Q: suppose f’(x)=x^4+x^3-6x^2. Determine the value of x where f has a relative maximum value.

A: The solution for the above question is as shown below.

Q: Express ax2 + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

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Q: Consider f(x) = 2x + 5, g(x) = x³ . fog = g of = %3D Consider f(x) = Vx² + 8, g(x) = x² + 8. fog =…

A: To find the value of f∘g=f(g(x)) substitute the g(x) in place of x in f(x) Similarly, to find the…

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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Q: Find the local maximum and minimum points of f (x) = (3x - 1)3.

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Q: Analyze the polynomial function f(x) =x-(x- 2) using parts (a) through (e).

A: Please find attachment for the details solution

Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

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Q: find and classify the stationary points of the function f(x)=x^3-2x^2+2

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Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

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Q: Find an equation of the cubic polynomial f(x) = ax3 + bx2 + cx + d that passes through the given…

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Q: Find the zero(s) of f. Ay -1 2 x f(x) = -2x2 + 3x %3D 2.

A: The function is given by  To evaluate : The zeros of the function fx

Q: If f(x) = x2 – 5x + 7, what are the co – ordinates of the minimum of y = f(x – 2)?

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Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: Let h(x) where f(x) = In(3x² + 2x + 2) and g(x) = -2x. What is h'(x)?

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Q: A​ once-popular children's doll is slowly declining in popularity. The quartic function…

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Q: Find the linearization L(x) of the function at a. f(x) = x4 + 6x2, a = −1

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Q: The quadratic function f(x) = a(x – hỷ² + k, a + 0, form. The graph of f is called a/an whose vertex…

A: A quadratic function is a second-degree polynomial function and the general form of a quadratic…

Q: The domain of the function f(x,y) = In(2 – /x2 + y² ) is: %3D - x² +y² < 4

A: The explanation of the solution as follows:

Q: Find the linearization at x = a. g(x) = 20x² x - 3 a = 12

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Q: . The function f(x, y)= 8x' - /4x* + 3y* is homogenous in x and y of degree -. The function f(x, y)=…

A: Here we have to find the degree of homogeneous function

Q: The function f(x) =is 1-z2 Is 9+z2

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Q: Find a cubic polynomial f(x)=ax3+bx2+cx+d that has horizontal tangents at the points (-5,2) and…

A: Calculation:Compute the derivative of y = ax3 + bx2 + cx + d as follows.y' = 3ax2 + 2bx +…

Q: Show that the function f(x)=x3−3x2+6x−1 is strictly increasing on R.

A: Let us find f'(x) using the power rule

Q: 3- Show that the function y = x3 + 3x + 3 satisfy the y" + xy" 2y 0

A: Function does not satisfy the given inequality. See the attachment

Q: 2. Let f(x) = 3x + 6 € Z7[x]. Find all associates of f(x).

A: The given function is fx=3x+6∈ℤ7x To find: the associates of f(x).

Q: Q3. At what points are the functions continuous y =-3x x+3 y = x2-3x-10' y = (2x - 1) X-2

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Find the linearzation L(x) of f(x)= \sqrt(5x+16) at a=0

A: Given Fx=5x+16 at a=0The objective is to find the linearzatin Lx ofFx=5x+16 at a=0find the…

Q: Show that f is linear of slope m if and only iff(x + h) - f(x) = mh (for all x and h)

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Q: Find the g (2) if g (x) = S VE– Idt %3D

A: gx=∫32x3 t-1 dt Now we need to find integration  gx =∫32x3 t-1 dt=23 t-13232x3=232x3-132-23…

Q: Find the formula of f(x) a polynomial function of a least degree

A: At x=-4 the curve cuts the x-axis. So x=-4 has multiplicity=1 So the factor is (x-(-4))=(x+4)   At…

Q: Use the Intermediate Value Theorem to show 11. f(x)=2x' +3x-1 has a zero between a = 0 and b = 1.

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Q: Let p=(12-2x)^2 for 0≤x≤3 be the price at which x hundred units of a certain commodity will be sold,…

A: Given: P=(12-2x)2         for 0≤x≤3            Revenue   R(x)=xP(x) then    R(x)=x12-2x2…

Q: Find a third-degree polynomial p(x) that is tangent to the line y = 14x − 13 at the point (1, 1),…

A: Let px=ax3+bx2+cx+d   →1 be the required third-degree polynomial. Differentiating with respect to x,…

Q: Find the linearization L(x) of f (x)=- Vx -5 at a =3. – 5 2.

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Q: 16. Let f(x) = x² + 10x + 28 m, find m if the function only has 1 (ONE) x-intercept. -

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Q: The linear function f(x) = ax + b is a constant function if?

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Q: Find f for the function z = - 3x6 0 02-30x4 ex ax = ex 7x8 1 8 6x 02-02-63 x = 6xy + 4y2.

A: This question can be solved using the concept of partial derivatives.

Q: 23) The domain of f(x) = Vx + 3 is

A: Consider the function

Q: t is the absolute minimum value of h(x) = -2x² %3D

A: Solution of the problem as follows

Q: Find the linearization at x = a. 1 f(x) = = 5 +3

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Q: Find the local extrema of the functionf(x)=x2+x−2x−2.

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Q: 2. Find and sketch the domain of the function: f(x, y) = In(9x² + 25y² – 225)

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Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…