Let h(x)=f(x)+g(x). If f(x)=6x4 and g(x)=9x7, what is h′(x)?

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: Sketch the domain of the f(x, y) = ln((x² + x² – 4)(16 – x² – y²)) |

A: Recall:  Domain of the function:           The domain of the function is the set of all values for…

Q: Find df/ dx of  f(x)=(x2-1)(x3+3x2/x2+2)

A:

Q: Find the linearization L(x) of the function f(x) = x^3/4 at x=256.  L(x)=?

A:

Q: Which is equal to (x) given that g(x) = 1- 3x and h(x) = V?

A:

Q: Find f′(x) and f′(c). Function f(x) = (2x2 − 3x)(9x + 4) Value of c = −1

A: f(x) = (2x2 − 3x)(9x + 4) c = −1   f'(x) = (2x2 − 3x).(9x + 4)' +  (2x2 − 3x)'. (9x + 4)        =…

Q: Find d2y/dx2 implicitly in terms of x and y.    x2y − 4x = 5

A: To find the second derivative of y implicitly in terms of x and y.

Q: A cell phone factory has a cost of production C(x) = 150x + 30,000 and a revenue function R(x) =…

A: Break even point is where total revenue equals total cost. Here total cost is given by…

Q: If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies…

A: It is given fx=x4, gx=x3, f'(x)=4x3 and g'(x)=3x2.

Q: Show that a cubic function f (x) = x3 + ax2 + bx + c is increasing on (−∞,∞) if b > a2/3.

A: Given function is: fx=x3+ax2+bx+c Then we get, f'x=3x2+2ax+b

Q: Q1. Find ý of the function x2 – e2x+3y – In(xy³) = 0. -

A: here is the solution

Q: Let h(x)=f(x)g(x). If f(x)=ln(3x2−2x−4) and g(x)=3x−1, what is h′(x)?

A:

Q: + iv is analyt: and satisfies the a real constant

A: Since f is analytic in S, it satisfies Cauchy-Riemann equations. Thus,

Q: Find h(0), h(x + 3), and h(-x) for h(x) = x + Vx² – 1. 2)

A:

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

A:

Q: What is the domain of f (x) = ln(x – 3) + 4?

A: Domain where fx is well defined.

Q: Find fxy when f(x, y) = 8xeXy.

A: To find fxy when fx, y=8xexy.

Q: If f(x) = ln ( v3x² +5 ), what is f'(x)?

A:

Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: Find the linear approximation of f(x) = x4 + 3x2 at a = 1.

A: We first find f'(a)=f'(1) f(x)=x4+3x2f'(x)=4x3+6xf'(1)=4(1)3+6(1)f'(1)=4+6=10   We now find f(1).…

Q: If a F (2) = xy+i (x² – y²), what is F (-1+2i)?

A: given  F(z)=xy+i(x2-y2) To find the value of  F(-1+2i)

Q: The function f(x,y) = 3x2 - 2xy + y2 + 8y has one stationary point. What is the location and…

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Q: If f(x) =3 ln x and g(x) = e2 , find go f(x). %3D

A:

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

A:

Q: find the linearization of f(x)=x^2+4x-4 at x=2

A: Linearization formula, L(x)= f(a)+f'(a)(x-a)

Q: What is the local maximum and minimum of the equation f(x)=x2e17x

A:

Q: t² - t dt 0, = (x)6 g'(4) =

A:

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

Q: Find the linearization of the function at x = 1.* f (x) 2x - 3x + 7 %3D

A: From the given problem:   fx=2x3-3x+7 ; x=1   As we know that the expression for linear…

Q: Let h(x)=f(x)g(x), where f(x)=ln(4x2−3x) and g(x)=3x−1. What is h′(x)?

A: GIVEN,     f(x) =ln (4x2-3x)                  g(x)  = 3x-1                  h(x) = f(x) g(x)

Q: The derivative of f(x)= (x2+2x)(x²-2x) is a. 4x3-8 O b. x-4x2 с. none d. 3.

A:

Q: Let h(x)=f(x)/g(x), where f(x)=ln(3x2 +2x+2) and g(x)=−2x. What is h′(x)?

A: Here we use quotient rule, which is pq'=p'q-pq'q2

Q: Let_y=x² +5x³-4x+1 then dy- ||

A:

Q: e. f(x) = 2* DA. O(x²) B. 2(x²) Oc. O(x²) . f(x) = [x][x] (floor of x times ceiling of x) DA. O(x²)…

A:

Q: Find the linearization L(x) of y = (64+3x2)-1/2 at a = 0. L(x) = %3D

A: The given function is: y=f(x)=(64+3x2)-12 So, f'(x)=-1264+3x2-32(6x)        =-3x64+3x232

Q: Find the linearization of f(x) = V16 – x² at a = 3. %3D

A: Given: The formula used for linearization:

Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

A:

Q: The y, of y'"-y=2x²-x -3 by using variation of parameters is: .A y,(x)=Ae*+ Be- .B Yp(x) = x – 1 .C…

A: Given that  y"-y=2x^2-x-3 To find the particular solution by using the variation of parameters

Q: If FIX) is an antiderivative of x-2 + x1, then what is the value of F(1) - F(-1)? A) 3 (в) -2 -1

A: Solved below

Q: Find the general solution of y" = 6y' – 9y where y is a function of x.

A: Given differential equation, y''=6y'-9y Find the general solution of the differential equation.

Q: What is g'(x) when g(x) = ln (x³ + 3x² + 5x + 6)?

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Q: E. y = xArctanx - In V1+x

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

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Q: Differentiate with respect to t 100 = x2 + y2

A: give equation ;- 100=X2+Y2 when we differentiate above equation with respect to t , we get

Q: Given the profit function P(x) = 1.3x – 0.01x² – 30, find the value of x at the function's optimum…

A: The profit function is: P(x)=1.3x-0.01x2-30

Q: Find the critical numbers of the function. a. f(x) = x3 + 6x? – 15x b. g(x) = V1- x2

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

A:

Q: If f(x)=x* and g(x)= x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule multiplies derivatives to…

A:

Q: In(x² + y² – 9) V25 – x2 – y? - Sketch the domain of f(x, y) -

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…