F(X) = x,3+x,3 – 3x,x2

Q: A function of the form y ax + bx + c, a + 0, is called a/an function.

A: The given function is, y=ax2+bx+c, a≠0 For the given function, the degree of the function is 2.

Q: Find fxx (x,y), fxy(x,y), fyx (x,y), and fyy(x,y) for the function f. f(x,y) = 5x e 8xy

A: Given function is f(x, y) = 5xe8xy

Q: Determine the nature of the stationary points of the function in the following case: f(x,y) = (x2 +…

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Q: Find y as a function of t if 9y" +12y + 29y = 0,

A: 9y''+12y'+29y=0which condition y(2)=8, y'(2)=9To Find: y(t)

Q: Find y as a function of t if: y''+8y'+97y=0 y(0)=9 y'(0)=3

A: Since the given differential equation is the second order linear homogeneous differential equation.…

Q: Which type of discontinuity does the function exhibit at x = 3? %3D (-x2 + 1, -1 sx<0 2х, f(x) =…

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Q: Evaluate the function at the specified points.  f (x, y) = x + yx^3, (2, 2), (−1, 4)

A: To evaluate the function at specified points:f(x,y)=x+yx3, (2,2),(-1,4) Solution: Given,…

Q: Joshua wants to find the local maxium and minima of the two variable function F(x, y) = x³ +y² – 48…

A: We will find out the required points.

Q: Find the linearization L(x) of the function at a. f(x) = x2/3, a = 27 L(x) =

A: The linearization of the function fx at x=a is Lx=fa+f'ax-a

Q: Find and sketeh the domain of the function f(x, y)= ln| xy - 1 Vy-x² ху —1

A: Given: fx,y=lnxy-1y-x2 to find the domain and sketch the domain of the function.  The domain is the…

Q: F(X) = 2x,?+x,2+x,?+6(x,+x,+X3)+2x;X,X3

A: Topic :- Differentiation

Q: find functions f and g so that f ∘ g = H.

A: given: Hx=1-x2 we have to find the functions f and g so that f ∘ g = H.

Q: evaluate the function at the specified points. f (x, y) = x + yx3, (2, 2), (−1, 4)

A: Given function is fx,y=x+yx3

Q: Classify the stationary point(s) of the following functions as convex, concave (strictly or weakly)…

A:

Q: Find y as a function of t if 5y′′+31y=0 y(0)=4,y′(0)=7y(t)=

A: The given differential equation is  5y''+31y=0   ......(1) and the initial condition is y(0)=4 and…

Q: Find y as a function of a if r'y" - 5ay + 9y = r, y(1) = 9, y'(1) = 3.

A: Given: x2y ''-5xy'+9y=x9, y(1)=9, y'(1)=3 Consider Homogenous differential equation  x2y''-5xy'+9y=0…

Q: Find y as a function of t if 8y′′+32y=0 y(0)=9, y′(0)=6.

A:

Q: Find the first and second derivatives of the function. h(w) = (w2 + 6w + 7)5/2 h'(w) h"(w)

A: The given function is h(w)=(w2+6w+7)52

Q: Find y as a function of t if y(0) = 7, (0) = 6. y(t) = = 49y" + 140y + 136y = 0,

A: The given DE is: 49y''+140y'+136y=0 So, the auxiliary equation of it is:…

Q: Sketch the curves of the following functions: 1. y= (x² – 1)* 2. y = x Vx + 1

A: y=xx2+1 To find x-intercepts, put y=0, we get ⇒xx2+1=0⇒x=0  or  x2+1=0⇒x=0  or  x2+1=0⇒x=0…

Q: Find the stationary points of the function: f(x,y,z) = 2*y*z + 7*x*z - z + 5*x*y + y x = ? y = ?…

A: The solution is given below

Q: Find an equation for the level curve of the function f(x,y) that passes through the given point.…

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Q: Find fxx. fyy fxy, and fyx for the function f(x,y) 4e*ty %3D

A:

Q: Find the fx(x, y) and fy(x, y) of the following function x2 — уз – y3 f(x, y) = Inxy

A: While finding partial derivative in multivariable function, if we have to find the partial…

Q: Find the direction in which the function is increasing most rapidly at the point P 0. f(x, y) = xy 2…

A:

Q: Find all points (x, y) where the functions f(x), g(x), h(x) have the same value: f(x) = 2x−5 + 3 ,…

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Q: The stationary points of the following function f(x, y) = (y-2) x²-y² is: .A (0,0) , (2,2) .B (0,0)…

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Q: Let g(x) = f(t) dt, where f is the function whose graph is shown. %3D y f 2 12 2.

A: The function f(t) in the interval (12,14) is a parabola. The vertex of the parabola is (14,6) and it…

Q: Find the indicated value of the function f(x,y,z) = 6x – 7y + 2z° - 3. f(3, – 4,2) f(3, – 4,2) =

A: The given function is, The values of x, y and z are,

Q: Plot the following functions 1. y = - V2x +1 2х + 1 2. y = (x – 1)3 + 2 3. y =-1 3. У 2x

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Show that the function f(1) = (e¯1 + 1)¯' satisfies y' + y² = y, y(0) = }.

A: To prove: ft=e-t+1-1 is a solution of given differential equation y'+y2=y.

Q: Which of the following is a stationary point of the function f(x, y, z) = x² – 2y? + yz + 2ay – z…

A: Given f(x,y,z)=x2-2y2+yz+2xy-z

Q: Find y as a function of t if 8y" + 29y = 0, y(0) = 5, 3'(0) = 8. y(t) =

A:

Q: Find the first and second derivatives of the function. h(w) = (w2 + 6w + 7)5/2 h'(w) = h"(w) =

A:

Q: Find a function y(x) such that 2yy' and y(2) = 5. y(x) :

A: Given that 2yy'=x   and  y2=5. Solve the above equation as follows.…

Q: Find y as a function of t if 7y" + 32y = 0, y(0) = 2, y'(0) = 4.

A:

Q: Find domain and range of the function f(x, y) = In[ e – x² – y°]

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Q: f(x) = 6x5 – 4x3 + 10

A: To classify the stationary points of the function: f(x)=6x5-4x3+10

Q: f(x) = x3+x

A:

Q: z = (x − 8)(y + 6)(y − 2) Find the stationary points of the function and determine their types

A: Follow the steps below to obtain the stationary points of z=f(x,y) . Calculate fx, fy , fxx , fyy ,…

Q: Locate the stationary points of the following functions and categorise them using second order…

A: z=f(x,y)=xey-2y+x22-3x..........(1)

Q: Find the function y(x) such that y′′(x) = 0 with y(1) = 2 and y′(1) =−1.

A: Given y′′(x) = 0 with y(1) = 2 and y′(1) =−1. y''(x)=0, with y(1)=2 and y'(1)=-1Now integrate both…

Q: Locate the stationary points of the following functions and categorise them using second order…

A: Consider the given equation. z=fx,y=xex-2y+12x2-3x   Find the derivative with respect to x and y.…

Q: Find all points (x, y) where the functions f(x), g(x), h(x) have the same value: f(x) = 2"-5 + 3,…

A: Given that, the functions are fx=2x-5+3, gx=2x-5 and hx=8x+10.

Q: Find y as a function of a if y(0) = 8, y(0) = 4, y"(0) = 134. y(x) = y"8y" -y + 8y = 0,

A:

Q: (d) Calculate the coordinates of the stationary points of the function z(x,y) = x³ – y³ – xy + 6.

A: We have to find the stationary points i.e., the critical points of the function zx,y=x3-y3-xy+6.…

Q: Find and classify all stationary points of the function f(x, y) = 2y³ + 6yx² – 3x³ – 150y

A: