The sum of two numbers is 8. Find the numbers if the sum of their cubes is to be minimal. The

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A: Here we have to write the equation of the curve that passes through the point (1,3) and has a slope…

Q: Find the equation of the line tangent to the graph of y = 2x - 8x2 + 2x -6 at x = 2. | %3D

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Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

A: Given that f(x)=x2 To find two tangents that passes through (-1,-3)

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Q: A line with a positive slope is parallel to one of th below.

A: From the graph of positive slope line, at x=0 , y= 3 at x = 4 , y = 4

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Q: What is the slope of the tangent line to the graph of the solution of y' = 5√y + 3x³ that passes…

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Q: What is the slope of the tangent line to the graph of the solution of y' = 6√y + 7x³ that passes…

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Q: Find the slope and equation of the line tangent to f (x) = x² – 4 at the point (3, 5).

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

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Q: Find the points on the graph of f (x) = x3 − 3x2 + x + 4 where the tangent line has slope 10.

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Q: What function should be used to minimize the distance between, y = 3x2, and the point (0, 2)?

A: y=3x2,  0, 2.

Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

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Q: What is the slope of the tangent line to the graph of the solution of y' = 5√y + 3x³ that passes…

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Find the exact length of the curve on the given interval. Show at least 3 steps to justify your…

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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 line y = -4x + 16 is tangent to the graph of 100 y : x + 6 at the point help (points)

A: Given the equation of a tangent line:

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: 4) Find the slope of the tangent line to the curve 4 y = 3(х3 — 2х2 + 3х — 5) at the point (2,) Give…

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Q: 6. Show that there are no tangents to the graph of 5+2 that have a negative slope. .

A: Given function:- y=5x+2x+2

Q: ction defined by f(x) = x2 – 3x + 4 at (-1, 2). Write

A: we have to find the slope of the line tangent to the graph of the function defined by  f(x) = x2 –…

Q: What is the slope of the tangent line to the graph of the solution of y' = 7√x + 6x³ that passes…

A:

Q: What points is the function y=|5x-1|+7sin(7x) continuous?

A: we have given function y=5x-1+7sin(7x) we know that  sin(ax) is continuous everywhere hence sin(7x)…

Q: Find the slope and y-intercept of the line through the point (4,10) that cuts off the least area…

A: We have to Find the slope and y-intercept.

Q: ind two numbers whose difference is 186 and whose product is a minimum.

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Q: The shortest distance from the point (5, 10) to the curve x2 = 12y is: 5.127 6.445 4.331 3.474

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Q: Compute the slope of the secant line containing the points (1, f (1)) and D) on the graph of f (x) =…

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Q: Find the slope of a line that is tanget to f(x)= 1/x at the point (2,1/2).

A: Given:

Q: Find the slope of the curve y=x^3-3 at the point ​P(-2,-11​) by finding the limiting value of the…

A: Given,y=x3-3Point P -2,-11The slope of the secant line ism=fb-fab-a

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: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A: We have to find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis…

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have vertical tangent line.

A: This question is taken from the tangent and line in which we have to all points on the graph that…

Q: The slope of the tangent line to the graph of the function y = 8Vx – 2 at (4, 14) is 2.00 3.50 -3.50…

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Q: If f(2) = 3 andf'(2)=-1, find the equation of the tangent line when x = 2 %3D %3D %3D

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Q: 1) Find the slope of the linels) tongent to the graph of (y+x)²-y =x² at X=0.

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Q: Determine the equation of the line passing through the point (3,22) which minimizes the area of the…

A: This question is based on application of Derivative. The two-point form of a line passing through…

Q: Show that the equation y^2=x determines an infinite number of implicit functions.

A: Consider the given equation: y2=xSolve in terms of y:y=±xSo, there are two functions that can be…

Q: Locate and classify all the critical points of the function.(If an answer does not ex g(x, y) = 4x2…

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Q: find the length of the curve y = 2x6+1/8x2 from x is greater than or equal to 1 and less than or…

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Q: Find an equation of the tangent line to the graph of y = 2x² + 3 that is parallel to the line 8x - y…

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Q: Find the number whose sum with its reciprocal is a minimum.

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Q: The slope of the tangent line to the graph of the function y = 8Vx - 2 at (4, 14) is . O-3.50 O2…

A: We will find the derivative of the function y and evaluate it at x = 4 to find the slope of the…

Q: Find the absolute maxiom and minimum. for F f(x) = Xe 10the interual

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Q: Find the slope and y-intercept of the line through the point (2,7) that cuts off the least area from…

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Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: What is the slope of the tangent line to the graph of the solution of y' = 3√√y + 7x³ that passes…

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Q: Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each…

A: To find out the critical points and denote it's nature.

Q: Find the slope and y-intercept of the line through the point (1,2) that cuts off the least area from…

A: Given : Point ( 1 , 2 )  It cuts off the least area from the first  quadrant

Q: Find the exact length of the curve over the given interval. 2sxs3 4x'

A: