Find all local maxima, local minima and salbl points for the function fcx.y) = y sin X

Q: Find all values of x for which f(x) = e?*(x² – 12) has horizontal tangent lines. %3D

A: Horizontal tangent meaning slope of those tangent are zero . Take the derivative and equate to zero…

Q: What is the y-intercept of the function y = cot I? || ㅇ(T,0) O (0,0) O (1,0) (0, 1) O It does not…

A: The function is given as y=cot(x) The objective is to find the y-intercept.

Q: find the domine of the function y(t)=sin 4t

A: Consider the given function: The domain of a function is the set of input or argument values for…

Q: Determine the missing coordinates of the points on the graph of the function

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Q: For what vaļue of x does the function g(x) =x - 2x? strictly convex? В. x> 0 A. x> 2 D. x -2

A: From the given problem:   gx=13x3-2x2   As we know that:   If f''(x)<0. then function strictly…

Q: The domain of f(x,y) = ln xy is points (x, y) in the first quadrant. Select one: O True O False

A: Domain  set of all input values where function defined

Q: (x) = 5sinx/6sinx+4cosx The equation of the tangent line to

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Q: Find the area A of the largest rectangle that can be inscribed under the curve of the equation below…

A: Given y=e-x2

Q: 4. Find if y is a function of r defined implicitly by da 2*y + sin a = xe" + In

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Q: Find Ta Centered at x 2 f(x)=e,a=0

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Q: Given the equation x In(y) = z Arctan(3*y). Assuming z as a function of variables a and dz find

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Q: (c) Find the tangent line equation to the curve x²y? = x + 2y at point (0,0). Use that approximation…

A: The given curve is x2y2=x+2y   To find the tangent line equation at point (0,0) Then, find the value…

Q: Consider the function y = f (x) = x² + 10 + 24 and the x-value xo = 5. %3D %3D (a) Find a formula…

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Q: Find the equation of the tangent line to the graph of f(x) = xcos(4x) at x= 4 Enter your answer in…

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Q: Evaluate fx and fy at the given point. f(x, y) = e¹³y sin(x), (π, 0) fx(π, 0) = (No Response) fy(π,…

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Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: Find the equation of the tangent line at y = 0, given,the inverse function x = (3y+ 2)V+1)2. %3D

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Q: Find the point P on the graph of the function y = Vx closest to the point (3,0) The a coordinate of…

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Q: Find the domain and range of the function f(x, y) = exy

A: Given information: The function fx,y=exy

Q: Use the value of the given hyperbolic function to find the values of the other hyperbolic functions.…

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Q: Find the equation of the tangent line to the function f(x) = -3x? – 2x at the point where x = 1.…

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Q: Ql. (a) Sketch the contour plot of f(x.v)=2 using the level curves of height k = -2, -1, 0, 1, 2.…

A: (a) Consider the given information. fx,y=yx Now, draw the contour for the given values.

Q: Find an equation of the tangent line y(x) of r(t) = (t',tº) at the point t = 1. (Use symbolic…

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Q: find the specific function values.ƒ(x, y) = sin (xy) a. ƒ(2, pai/6)  b. ƒ(pai, 1/ 4 )

A: a) Plug x=2 and y=pi/6 and then simplify

Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find the smallest positive c for which (c,0) is an x-intercept for the function f(x) = tan(1.58x).…

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Q: The len for th function Y= Fcx), where f is arc Curye increasèng function, J Ise tio' de. Vst tio'…

A: The arc length of curve y = f(t) is given by: S(x)=∫0x 1+dydx2 dx

Q: At what points are the functions continuous?

A: The function can not have a negative value under a square root.  But x^4+1 > 0 for all values of…

Q: Given the function f(x)=−2xcos(x), find f′(x). Then find the equation of the tangent line at at the…

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Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: Find all points on the curve where the tangent line has the given slope. (If an answer does not…

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Q: The function is z = Determine ე3 2 əyəwəx wx²y + xy² + tan (wx)

A: A value or values that, when substituted for a variable in an equation, make the equation true.

Q: Determine the value(s) of x for which the line tangent to f(x) is horizontal. (Enter your answers as…

A: Given,

Q: Find the x-coordinate of each point where the function f (x) arcsin (5 a - 2 x) has a horizontal…

A: For horizontal tangent, equate slope of tangent = 0 Slope of tangent = f'(x)

Q: Find all values of x for the given function where the tangent line is horizontal. f(x) D (x² + 7) *…

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Q: Given the equation x + 4xy + y* = 8, evaluate dy Assume that the equation implicitly defines y as a…

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Q: Find the maximum and mini- mum values of the function. y = sin x + sin 2x

A: Given: y=sinx+sin2x for finding maximum and minimum value of given function, we draw graph of it as…

Q: Given the implicitly defined function sin(r²y³) + y³ = r + y I dy dy and dx2 find at the point (x,…

A: Topic = Derivative

Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

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Q: Match the functions with their periods. y = sin(z - T) y = -csc2r y = 5cot -8 y = -6cotr – 10 y =…

A: Given: y=25sinx-πy=-13csc2xy=5cotπ--8y=-6cootx-10y=5sec(2x+2π)y=-3tanx2

Q: f(x,y) = x [(In x)2 + y2] %3D find the extreme points of the function

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Q: Find the parameter k such that the function y cos(kx) satisfies the equation y + 5y" = 0.

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Q: The curve y= f(x) passes through the three points (1,3), (2,8.5), and (3,44). Estimate, as accurate…

A: The given problem is to estimate the first derivative of f(x) ,dy/dx at x=1.5 for the curve y=f(x)…

Q: Find the smallest positive c for which (c,0) is an x-intercept for the function f(x) = tan(1.46x).…

A: The given function is: f(x)=tan(1.46x) To find the smallest positive c for which (c,0) is an…

Q: Find the point on the curve f (x) = Vx that is closest to the point (2,0). Put your answer in the…

A: Use distance formula and differentiate and put zero

Q: Find the function f(x,y,z) with a magnitude y.

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Find the absolute maxima and minima of the function f(x,y)=x²+y? on the closed triangular region…

A: The given function is fx,y=x2+y2 Given lines are x=0,y=0,y+2x=2