Q.27 A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct exterma for the curve 3x- 16x3-24x + 37 iS

Q: If the given curve 6y = x + 9x2 + 12, what are its minimum and maximum points of the curve? Show…

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Q: (b) Determine the position and character of the double points on the curve x³ + x² +y² – x – 4y +3 =…

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Q: Where is the global minimum of f(x)? \f (x) + 17 x8 I10 Figure 4.4 (a) x1 (Б) хз (c) There is no…

A: Global minimum is the point for which function has absolute minima.

Q: 1 2 #5) A) Find the length of a curve y Inx for 3 < x < 7. 4

A: L= integration of sqrt of 1+ (dy/dx)2 dx from a to b

Q: 4. The graph of f(x) = -3(x – 2)² – 6 is a parabola that %3D opens with its vertex at (L, ), and…

A: Given: The function fx=-3x-22-6, To determine: The given blanks in the following statement, "The…

Q: 7. Find the exact length of the curve: y = 1 + 6x³/², 0 < x < 1.

A: The length of the curve is calculated from the graph.

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

Q: 5 Let glx, ,x -x + 16x, -4x3 . Firid the stationary points and detesmie if t is a maximm saddle…

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Q: Find the points on the circle x? + y? = 1 in which f(x, y) = 4xy has an absolute maximum and the…

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Q: Find the maximum and minimum values of the function ƒ(x, y) = 3x + 4y on the circle x2 + y2 = 1.

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Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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Q: b) How far should we let 0 run to traverse the curves one time only?

A: To find how far θ needs to run in order to traverse the the the curve one time only, we need find…

Q: 1. Find the minimum point of the following curve. Express your answer in this form (#,#) or N/A if…

A: We will use the fact that the derivative of y with respect to x is zero at the point of extrema. The…

Q: Given ƒ(x) = ax2 + 2bx + c with a &gt;0. By considering the minimum, prove that ƒ(x)&gt;= 0 for all…

A: Consider the given function f(x) = ax2+2bx+c with a &gt; 0It is required to prove that:

Q: The graph of f(x,y)=+ 1 +76xy has One saddle point only. O One local minimum point and one saddle…

A: For the given equation

Q: 1 find all points lif any) of hxizantal and vertical paints of to the curve tangency X={^_f +2…

A: Given that: x=t2-t+2,   y=t3-3t To calculate dx/dt, ddtx=ddtt2-t+2=ddtt2-ddtt+ddt2=2t-1+0dxdt=2t-1…

Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

Q: 1(4) = , re) = -2 x + 2 2(т — 1) 3 f' (x) = 3 and f"(x) = %3D 2(x – 1)2' (x – 1)³ * Find all local…

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Q: Find the extreme values of g(x,y,z) = 2x² + xy + 4y² + xz + z² + 2. %3D and determine whether the…

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Q: б. (a) Sketch the level curves z = k for k = 0, 1, 2 if z = x2 – y?.

A: The level curves of a function f of two variables are the curves with equations f(x, y) = c, where c…

Q: a) Let f(x,y) = ye2x. Find an equation of the level curve that passes through the point (-In 2,2)…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: on a curve is said to be an extremum if it is a local minimum or a local A point maximum. The number…

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Q: (1) Find a point P in the first quadrant on the curve f(x) = such that the rectangle with sides on…

A: In the question we have to find the perimeter of the rectangle.

Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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Q: If f'(x) = x(x – 1)(x + 3)*, then f(x) has a local minimum at: Select one: а. х%3-3 only b. x = 0…

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Q: The graph of f(x,y)=++13xy has X y -13ху O One local maximum point only. O One local maximum point…

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Q: 9 Find the length of the curve x = on 3sys5. %3D 27' 4y The length of the curve x = 9 - on 3sys 5 is…

A: We have to find arc length of give curve.

Q: A point on a curve is said to be an extremum if it is a local minimum or a lo maximum. The number of…

A: Given that: f(x)=3x4-16x3+4x2+37

Q: For what values of k does the family of curves =² + (y – c)² = kc² have an envelope?

A: Eliminate C from f and f'c

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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Q: The graph of f1x2  31x  222  6 is a parabola thatopens , with its vertex at 1 , 2, andf122  is…

A: to find the vertex of the parabola

Q: Determine the location of each local extremum of the functio f(x) = -x°+ 1.5x? + 36x + 2 %3D O a.…

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Q: If f '(4) = 0 and f '(x) 0 for 4 < x < 5 then f has a local minimum at x = 4. True False

A: If f '(4) = 0 and f '(x) &lt; 0 for 0 &lt; x &lt; 4 and f '(x) &gt; 0 for 4 &lt; x &lt; 5 then f has…

Q: Consider the following. (If an answer does not exist, enter DNE.) h(x) = 5x3 - 3x5 %3D (a) Find the…

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Q: 18 The curve y = (x + 2)2 has a minimum point at A (0, 4). B (4, 0). (0, -2). (-2, 0).

A: for minimum point put f'(x)=0and solve the question.

Q: 1. Find the maximum point of the following curve. <press your answer in this form (#,#) or N/A if…

A: Differentiate the given function with respect to x and then solve y'= 0 to obtain the critical…

Q: The graph of x + z² = 1 is an ordinary right circular cylinder. Indicate axis of the cylinder lies…

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Q: Given f(x, y) = x² - 4y, the parabola x² - 4y - 2 = 0 is the level curve of fat 02 0-2 01 00 None of…

A: Ggg

Q: 8 For each of these curves, find the coordinates of any stationary points and state whether the…

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Q: 1. Find the absolute minimum and maximum values taken by the func- tion f(x, y) = x² + y² – x – y +1…

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Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: 3) Find the exact length of the curve y = x² – In x for 1< x < 2. 1„2

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Q: Find the exact length of the curve. y = In (1 - x2) ,    0≤   x ≤ 1/2

A: Given, y=ln1-x2,0≤x≤12 We know the ars length formula is, L=1+dydx2dx Now we find the derivative by…

Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12

Q: The graph of f1x2  31x  222  6 is a parabola that opens, with its vertex at 1 , 2, and f122 is…

A: To find the graph of the given function                         f(x)=3x-22-6 and to find the vertex.

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x + 4) in the interval…

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