Q1) Sketch and Find all critical points, local minimum and maximum, concavity, concave up and Concave down and inflection point. y= 4x -12x Q2) Write an equation for the tangent line at x 2 of the curve f (x)=(2x-1)²

Q: Find all points (x, y) on the graph of g(x) = x3/3 -3x2/2+1 tangent lines parallel to the line 8x -…

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Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

Q: 19. Does the line that is tangent to the curve y = x3 at the point (1, 1) intersect the curve at any…

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Q: Given S(x) = x* –12x². i) Find if exist, the maximum and minimum points of the curve by using second…

A: We will use the second derivative test to find the maximum and minimum points of the curve.

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

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Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

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Q: Determine any critical points, point of inflection and trace the curve. 1. y= 2x +3x –12x +7

A: Given y=2x3+3x2-12x +7   Dear Learner We expert are following Bartlbey Experts Guildlines so we can…

Q: Q2: Given the derivative f'(x) = x²(x³ - 3), find: (a)The critical points. (b)The stationary points.…

A: Given the function

Q: Find all points (x, y) on the graph of ƒ(x) = 3x2 - 4x with tangent lines parallel to the line y =…

A: Since the tangent is parallel to y = 8x + 5. Hence, the slope of the tangent = slope of the line = 8

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

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Q: Find the orthogonal trajectories for the family of curves x2 − 2y2 = C . Use a graphing utility to…

A: Concept: Trigonometry is used in finding distance and angles, there are six trigonometric ratios…

Q: Determine the coefficients a, b, c, d that will make the curve y = ax3 + bx2 + cx +d passes through…

A: Given y=ax3+bx2+cx+d

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: I dont know where to start this problem. It would be great to have some help

A: Given:

Q: y= (1-х):

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Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

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Q: Find the orthogonal trajectories for the family of curves y2 = Cx3 . Use a graphing utility to graph…

A: Given curve is y2=Cx3.

Q: Find the point (xo, Yo) on the graph of y = x³ + 3x² + 5x – 3, at which the slope of the tangent…

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Q: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

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Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

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Q: Find the point (xo, yo) on the graph of y = x³ + 3x? + 8x – 3, at which the slope of the tangent…

A: To find the slope of the function we need y'y=x3+3x2+8x-3y'=3x2+6x+8

Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

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Q: Find the point (x0, yo) on the graph of y = x + 9x² + 8x – 5, at which the slope of the tangent line…

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Q: Find the point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has…

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Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: find all points (x,y) on the graph of f(x)=3x^2-5x with tangent lines parallel to the line y=7x+1.

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Q: Find the critical points of y= -2x^2 +4x +3 and apply the Second Derivative Test to find the maximum…

A: Critical point and extreme points

Q: Determine any critical points, point/s of inflection and trace the curve. y = x2(2 - x2)

A: Here we use concept of derivative

Q: Determine any critical points, point of inflection and trace the curve. 2. y = x°(2– x²)

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Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: Determine the critical points of the curve y = x³ – 5x2 - 36 x + 25.

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Q: 4. Find the slope of the given function y3 = 4x with points (1, 2) using long method. Plot the curve

A: The solution are next step

Q: Determine any critical points, point of inflection and trace the curve. 2. y =x*(2-x*)

A: Here we use the concept of derivatives.

Q: Find the critical points of y= 2x^3 +3x^2–12x and apply the Second Derivative Test to find the…

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Q: Find the point (xo, yo) on the graph of y = x + 9x2 + 3x - 4, at which the slope of the tangent line…

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Q: Determine any critical points, point/s of inflection and trace the curve. Question 1.    y = 2x3 +…

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Q: 4. Determine the constant a,b, c, and d so that the curve defined by f(x) = ax³ + bx² + cx + d has a…

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Q: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

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Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

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Q: Find the length of the curve between the specified interval: 3/2 a. y = x7² from x = 1 to x = 4 b. y…

A: (a) Given curve: y=x32 Interval x=1 to x=4 The length of the curve is given by the formula:…

Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

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Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

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Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

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Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

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Q: Find the critical points/max/mins: Of the curve: y=2xln(x)-x2

A: I am attaching image so that you understand each and every step.

Q: Find the equation s for the perpendicular trajectories of the curve family. 1. x -

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