Use a graph to estimate the coordinates of the lowest point on the curve $x=t^{3}-3 t, y=t^{2}+t+1 .$ Then use calculus to find the exact coordinates.

Q: a particle moves along a curve y = (2x² + 5x)°, calculatey (0) and what is the interpretation of the…

A: Let us considre the function y=f(x) The derivative the function is denoted as dydx=f'(x) Derivative…

Q: Find the slope of the tangent line to the curve (a lemniscate) 2 (x + y ²)² = 25 (x² – y²) at the…

A:

Q: Find the shaded area of diagram that shecked by curve y = x2 + 2x and the line y = -x.

A:

Q: Differentiate (x-2)2+(y-3)2=9 at (7/2, ((6+3√3)/2)). Then use it to determine the equation of the…

A:

Q: Find the second derivative of the funcion. y%3D

A:

Q: You are asked to find the equation of a horizontal tangent line to the curve y=3x3+2ex+2x. Use…

A:

Q: What is the value of the slope of the tangent line to the curve *y+y<=5 passing through the point…

A:

Q: On the curve y3Dx2 ,find a point at which the tangent is parallel to the chord joining (0,0) and…

A:

Q: Find the slope and equation of tangent line y=4-x^3, (-1,5)

A: Consider the given equation: y=4-x3 The point where tangent has to be calculated is (-1,5)

Q: Find the points on the curve y 2x3+ 3x2- 12x + 9 where the tangent line is horizontal. (x, y)…

A: The above question is answered below

Q: Find the equation of the tangent line to the curve y = (2? - 8)' at point (5, 2). y =

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The Gateway Arch in Saint Louis is modeled by the curve: y = 210 − 20 cosh ( x/30) . At what height…

A: yx = Height of the Gateway archyx = 210 - 20coshx30         Blue curve---------------------formulae…

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 equations of the tangents to the curve x = 6t2 + 2, y = 4t3 + 2 that pass through the point…

A: Given data:     The first equation is: x=6t2+2. The second equation is: y=4t3+2. The given point is:…

Q: A point moves along the curve y = √x in such a way that the y-value is increasing at a rate of 2…

A:

Q: ie point where x (-)- %3D

A: Maxima and minima: f(x)=x2+kxWe should find the value of f'(x) Then we calculate the value of x for…

Q: find the slope of tangent line to curve y^2+x^2=y^4-2x at (-2,1)

A: Given function y2+x2=y4-2x  We have to find slope of tangent line at(-2,1).

Q: Average velocity is equal to the slope of a secant line through two points on a graph. Which graph?

A: Average velocity formula is:

Q: For the curve 3e arcsin (y) + 2 (x² + y²) = 2, find the slope of the tangent line at the point…

A:

Q: Find one point on the curve where the tangent line is horizontal y2=x3-3x

A: We have the equation of given curve as y2=x3-3x Now, the slope of the tangent can be calculated as…

Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

A:

Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: What are the coordinates of the point on the curve f(x)=4/x^2  -x where the tangent is horizontal?

A: Given:  f(x)=4/x^2  -x

Q: Inc is perpendicular to the linez =7 at the point where The tangent line to the graph of y

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

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

A:

Q: Find the equation of the tangent line of funclion y= ²+1 23 -2 at (40,- 73)

A:

Q: Find the point on the curve y=lnx such that the tangent line pases through the point (2,4). Need to…

A: Given The equation of curve is   y =ln x The tangent line passing through (2,4)

Q: Find the equation of the tangent line to the curve y = xV13 – x² at the point (2,6).

A:

Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

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

A:

Q: find the x-coordinates of the point on the curve y=2x^3-3x^2-36x-1 where the tangent is horizontal.…

A: For finding tangent is horizontal take slope 0

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: Find the equation of the tangent line to the function f(x) 8vx - 4 at the point (64, 60). Provide…

A: Calculate the slope of the given function;

Q: Find an equation of the line tangent to the curve at the point (4, 0.4). 2Vx ソミ x+6 Equation:

A:

Q: Find the tangent line to the curve 2y + " = ye"-2 at the point (2, ). %3D Please select file(s)…

A:

Q: Describe the tangent line at an arbitrary point on the “curve” y = 2x + 8.

A:

Q: Find the point in the first quadrant where the line y=2x intersects a circle of radius 3 centered at…

A:

Q: A point on a circle travels 5 centimeters in 2 seconds. Find thelinear velocity of the point.

A: Given: A point on a circle travels 5 centimeters in 2 seconds. To find: Linear velocity of the…

Q: 4. Center at (-4,9), tangent to the x-axis 5. Center at (-4,9), tangent to the y-axis

A: In this question we have to find the equation of the circle tangent to the x-axis and y-axis.

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: ength of the curve 1 1 < x < 2. 6 10x3 +

A:

Q: Find the point on the curve y = 3x + 4 which is closest to the point (5, 0). Preview Preview

A: Let (x, y) be the point closest to the point (5, 0) We will calculate the distance between these two…

Q: Calculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. x²+ y²-4x…

A:

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: find the acute angles between the curves y=6x6-17x5-33x4-28x3 and y=95x2+79x+90 at their points of…

A:

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 area bounded by the curve 4 square units 8 square units 16 square units 10 square units =…

A:

Q: Determine the slope of the tangent line to the curve y=2 – x2 at the point (3,-7)

A: slope of tangent = slope of given curve  step 1  we have to find slope of curve  slope = dy/dx  so…