h of the function, y %3D bel your axes clearly. (x)103

Q: Find the maximu rate of change of the function f(x, y) = x2 + xy+y at the point (-8, -7). V1013 3114…

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Q: tind the domain and range of y: sech X find the derivahive of

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Q: C. If h(x) = [f(x)]² + g(x),what is the equation of the line tangent to the graph of h at x = -2?…

A: First we will find derivative of h(x) at x=(-2) that gives the slope of the required tangent.

Q: c. f(1) d. Is f differentiable at x = 3?

A: Given The graph of function f as  To find: c. f1d. is f differentiable at x=3?

Q: Determine the relative extrema of f(x, y) = 2r? + y? + &r – 6y + 20.

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Q: E 8 10 6. F What is the tangent ratio for ZF ?

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Q: S(r) = x – 2:r +4 What is the y-intercept of the tangent line that intersects the function at I= 2?…

A: We know that,The tangent point of the given curve can satisfied the equation of that curve.

Q: y = f(x) cross-section y = g(x) base view

A: Solution...

Q: 4 The function f(x,y) = corresponds to x² + y? plot [ Select ] level curve [ Select] >

A: Here, the given function is: f(x,y)=4x2+y2

Q: Find the direction in which the function is increasing most rapidly at the point Po. f(x.y) = xy? -…

A: Given,     f(x,y)=xy2-yx2

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: dy for the function y = dx 7) Using the first principles definition, determine 2x

A: topic - derivative of a function

Q: For what value(s) of x does the graph of f(x) = 6x³ + 9x² – 216x %3D e a horizontal tangent?

A: To find the values of x does the graph of fx=6x3+9x2-216x have a horizontal tangent.

Q: y of f. 2. f"(x) 3 Concave down:

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Q: .3 ax when x= For what values of a and b is the line -3x + y = b tangent to the curve y 4? b

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Q: The volume of a right-circular cone of radius r and height h isV = π/3 r2h. Suppose that r = h = 12…

A: Consider the given: Volume,V=π3r2hr=h=12 cmDifferentiate w.r.t. "r",dV=π32rdrh    ⋯⋯11cm increase in…

Q: 4. What is the slope of the curve of f(x) = v2x + 1 at x = 4? а. 3 b. - с. d. ! e. None of the above

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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: S(r) = 2r2 +3r+2 What is the y-intercept of the tangent line that intersects the function at I= 2?

A: f(x)=2x2+3x+2

Q: Evaluate dy and Ay for the function below at the indicated values. y= f(x)= 44 1-- x- 2, dx Ax = -…

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Q: 0. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

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Q: Find the acute angle that the curve y = 1 − 3x3 cut the x axis.

A: The given curve  y=1-3x3 When it cuts the x-axis, y=0 1-3x3=0x=1313

Q: dy -from the function y= sint, x= cost as a parameter. da? Obtain

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Q: Find the slope in the x-direction at the point P(0, 2, f(0, 2)) on the graph of f when f (x, y) 3(y?…

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Q: Find the point at which the line y = 8x – 31 is tangent to the graph of y = eXf-16). %3D The point…

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Q: The formula for solving for the area in the first quadrant bounded by y = x², the circle x² + y² =…

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Q: %3D 42. Find f(x) dx for each graph of y = f(x). (a) y. (b) y 2. 1. 3 aronh of flr) = 2x + 3 and

A: Given query is to find the valuebof intgy from the graph.

Q: 30. f(x) = |x|; reflection in the y-axis followed by a translation 3 units to the right

A: 28. Given,                                f(x)=xTranslation 3 units down followed by a vertical…

Q: (B): The Trapezoidal rule for f(x)dx 5 and Midpoint rule f(x)dx = 4 .What value does Simpsons rule…

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Q: Find- for the following function dx x=a(cost + t sint).y=a (sint-tcost)

A: y=a(sint-tcost), x=a(cost+tsint) To find dy/dx.

Q: Q2) A/ Find the values of a and b if the equation of tangent at (2,3) on the curve y? : ax³ + b is y…

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Q: w For what values of x is the tangent line of the graph of f(x) = 6x' + 27x² – 71x – 54 - parallel…

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Q: Is y = |x| differentiable at x = 0? Justify your answer.

A: We are asked to check the differentiability y=|x|  at x=0

Q: of the curve yln x + 5x² + y' =13 at the point (1,2) dx b) Find

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Q: nd the point of inflection and discuss the concavity of the graph of the function. f(x) = sin , [0,…

A: Follow next step

Q: Find the x-coordinate of the inflection point(s) of y = f(x)

A: The function is called concave up in an interval if the opening is upside of the graph.

Q: Q4:Find the relative extrema of f (x) I+3 I- 2

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Q: Q. Find the length of the arc of the curve f(x) =+3,

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Q: c) Find the inflection points. х, у) . (smaller x-value) %3D

A: Given that: The equation of the function if f (x) = 3 sin (x) + 3 cos (x) , 0 ≤x≤2π . The critical…

Q: Q3 Find the equation of the tangent line to the function f(r) =x+7 at r 1. Show your work.

A: f(x) =x3 +7 Let y = f(x) = x3 +7, we have to find the tangent at x=1 , so value of y at x=1 is  f(1)…

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

A: Given query is to find derivative of the given expression with respect to x.

Q: If z is directly proportional to y and z = 48 when y = 6, %3D ty a. find an equation relating y and…

A: Given query is to find the relation between z and y.

Q: Find any relative extrema. 3 f(x,y) = x° - 12x +y? °-12x + +y²

A: Given: Function f(x,y) = x3-12x+y2 To find: Relative Extrema of the function (if exist) Concept…

Q: Q4) r(x,y) = x'/s – ½y? is harmonic ? Does the function %3D

A: The given function isf(x, y)=x13-19x-53y2to check the function is harmonic?

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: Estimate the slope b t the pótst a,where *3 9. X= 2 feck)- Estimate the arca above the x-asxis and…

A: