a. Discuss the curve P(x) = x^4 − 6x^2 with respect to concavity, points of inflection, local maxima and minima and the intervals where the graph is seen increasing or decreasing. b. Use the information obtained in 3(a) to sketch the curve.

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: At which points on the curve y = 1+40x3 – 3x does the tangent line have a locally maximum slope? A…

A: Solve the following

Q: 3. Determine the slope of the tangent at x = -1 on the graph f(x) = (5x² + 1)3.

A:

Q: 5. Find the equation of the tangent line that passes through point (1,2) to the graph 8y3 + x²y – x…

A: Proceed as shown below...

Q: 9. Find the family of the curve whose slope at any point is V√x + √x and also the member which…

A:

Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

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

A:

Q: Find the x Coordinate of the point on the graph of 4=x² where the to the Secant. Longent tine.…

A:

Q: 6. A rancher wants to fence off a rectangular corral with an area of 4050 sq. yds next to a river.…

A:

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

A: Given          5x2-4y2=C       Differentiate w.r.t to x       10x-8y dydx=0…

Q: 4. Find the slope of the tangent to the graph of f (x) = x³ + 3x² + x at its point of inflection.…

A: Slope of the tangent is obtained by dy/dx

Q: 5. Hance sits at one of the points on the curve y = 2x³ -3x²-12x +20 where the tangent is parallel…

A: Please see the below picture for detailed solution.

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

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

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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: Sketch the curve if y' is negative and y'' is negative on the interval of (-infinity, -3) with a…

A:

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: 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: 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: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

A: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

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

A: Given:

Q: Find the equation of the tangent line to the graph of y = 2x - (4 / √x) at the point (4, 6).

A: Given,            y = 2x - 4x and Point is 4, 6

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: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

Q: 4)Solve for the family of curves of straight lines with y-intercepts thrice as their corresponding…

A:

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

A:

Q: Jse the guideline in §4.4 to sketch the curve: f(x) = 2x3 + 3x2 – 120x. 4). Domain, Symmetry,…

A:

Q: At whhat point on the parabola y = x - 3x-5 is the tangent line parallel to 3x-y 2

A: Given y=x2-3x-5 To find the tangent line parallel to 3x-y=2

Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

A:

Q: 7. Find the equation of a line tangent to the graph of f(x) = cotx at x = π/4. Show all steps to…

A: Given :fx=cotx

Q: 2. Find the slope of the tangent to the curve y = 3 + 4x² - 2x³ at the point where x = a

A: given,y=3+4x2-2x3

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: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

A:

Q: 7. Find the slope of the tangent line to the graph at (1,1): x2y? - 9x2-4y2 = 0 x-9-4-0 (-4, 2/3)…

A: x2y2−9x2−4y2=0 Use implicit differentiation to find the slope of x2y2−9x2−4y2=0 Implicit…

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: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

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

A:

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

A:

Q: 9. Find the family of the curve whose slope at any point is √x + √√x and also the member which…

A:

Q: Two different level curves of the graph of z = f(x, y) can intersect. True False

A:

Q: 2. Determine the equation of the line tangent to the graph of y = x³ + 2x at the point (1,3).

A:

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

A:

Q: Determine the area of the triangle formed by the tangent to the graph of the function y=3-x2 drawn…

A: Given,            y = 3 - x2 , and the point 1, 2

Q: 4. Find the member of the curve whose slope at any point is 4y point (3, 4) and passes through the

A: Note: As they are different questions, as per our company guidelines we are supposed to answer the…

Q: 1 Find the length of the curve ソ= 9 from x =1 to x=2. 28x7,

A: