6. A rancher wants to fence off a rectangular corral with an area of 4050 sq. yds next to a river. No fencing is required along the river. Find the dimensions of the corral which will minimize the amount of fencing required. Justify your result using the 2d Derivative Test

Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: Estimate the slope of the tangent line to the graph of f(x) = x^2+6x at x = 5.

A:

Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

A:

Q: Section 2.4 Chain Rule Please show & explain all work, thank you.

A: Multiply both sides by x^2.

Q: What is the slope of the the tangent line to y=1/x^5+−1/x^3 at x=1?

A: Given y=1x5+-1x3 and x=1

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 3  where the tangent line is horizontal.

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 7x +…

A:

Q: Find the points on the curve y = 2x3 + 3x² – 12x + 7 where the tangent line is horizontal.

A: Given,          The points on the curve y=2x3+3x2-12x+7 where the tangent           line is…

Q: Find the slope of the tangent line at the point P = (1, 1) on the graph of              ex-y = 2x2 -…

A: Given,          ex-y = 2x2- y2    at   P=(1, 1)

Q: Find an equation of the tangent line to the curve y= x3 – 3x2 + 5x that has the least slope.

A: Given    slope is 1st derivative

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

A:

Q: Find the points on the graph of f (x) = 12x − x3 where the tangent line is horizontal.

A: The slope of the tangent line to the function is given by f'(x) . According to sum rule of…

Q: Find the slope of the tangent line to the graph of the functiony=f(x)=−6.5x^2 at point x=7

A:

Q: Find an equation of the tangent line to the curve  y = x sq root of x  that is parallel to the line…

A:

Q: Show that the curve y = 7e* + 3x + 2x³ has no tangent line with slope 2.

A:

Q: Find the equation of the tangent line at x=9 for f(x) =X^3/2

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

Q: What is the slope of the tangent line to the graph of x^2-xy+3y^2-2x+4y=3 at (3,0)?

A: The objective is to find the slope of the tangent line to the graph of x^2-xy+3y^2-2x+4y=3 at (3,0).…

Q: What is the slope of the tangent line to the curve y = 2sin 4x at x = 4

A: Given, The curve  y = 2sin4x   We have to find the slope of the tangent line to the curve at x = π4.…

Q: Locate the point where the slope of tangent line to y=In 2x2 IS-1- O (-1, In 2) O (-2, In 8) 3 In 4…

A: Given; y= ln 2x2.

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x)=6x2+2x+3…

A: The limit definition of derivative is given by: We know that f(x) = 6x^2 + 2x + 3  Now we will find…

Q: Find the slope of the tangent line drawn to the graph of −4x^2−xy+3y^3=−200 at the point (−1,−4).…

A: Given function is : -4x2-xy+3y3=-200 To find out slope of tangent dydx at -1,-4 Differentiating…

Q: Find the slope of the tangent line at given point 2x2 - 3y = x at (1.5,1)

A: First derivative of the equation curve give slope of tangent line to the curve.

Q: Find the points on the curve y = 2x3 + 3x2 12x + 8 where the tangent line is horizontal. (х, у) %3…

A: Given curve is : y = 2x3+3x2-12x+8 Tangent line is horizontal at points where slope=0

Q: 3. Find an equation of the tangent line to the curve at x=4 y=(sqrt(x)) / (x+6)

A: Given equation of the curve y = xx+6  ...............(1) Let the equation of the tangent at (x1, y1)…

Q: 6. What is the slope of the tangent line to the inflection point of the curve y = x3 – 4x2 - 3x – 6?

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the equation of the tangent line to the curve y=lnx2 that is parallel to the straight line y=x.

A:

Q: Find the slope of the tangent line at the indicated point * y = Vx2 – 2x at x = 3

A: Here, y=x2-2x So, the slope of the tangent at x=3 is: dydxx=3

Q: Find the equation of the tangent line to 4x2 +y2= 8 at (1,2)

A:

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 2x +…

A:

Q: *(1,). What is the equation of the line that is tangent to the graph of y = at (x³ + 1)?

A: We can find the equation of line as below.

Q: The point on the graph of f(x) = 1 where the tangent line is parallel to the line 3z + y = 1 is: %3D

A:

Q: Show that the curve y = 6x + 6x - 3 has no tangent line with slope 2.

A:

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 6  where the tangent line is horizontal.

A:

Q: Find the points on the curve  y = 2x3 + 3x2 − 12x + 2 where the tangent line is horizontal

A: To obtain the points where the tangent line is going to be horizontal to the curve, we need to find…

Q: The slope of the tangent line to f(x) = 3x² – 1 at x = 2 is 12. true false

A: The solution of the problem is given in the next step.

Q: Find the slope of the tangent line to the curve y = (1+ 4x)7 at the point x = 2. %3D

A: Slope of the tangent line is obtained by just derivative of the function  wrt the independent…

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

A:

Q: Find the equation of the tangent line on 3xe™v² - ez 2ye at (1,1)

A: Given  3xexy2-ex3=2yex2first we find dydx at point (1,1)

Q: Compute for the interval [2, 7], where y = 3x - 3. Ay Ax Ду Дх What is the slope of the tangent line…

A: we have y= 3x-3at x=2y=3×2-3 =3at x=7y=3×7-3 =18so,∆y∆x = change in y over the intervalchange in x…

Q: The slope of the tangent line to √x+y+√√xy = 2y at the point (2,2) is:

A:

Q: Show that the tangent line to the curve at y = 3x²+ 6x− 5 the point (−1. −8) is horizontal.

A: To show: That the tangent line to the curve at y=3x2+6x−5 the point -1,-8 is horizontal. Concept…

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

A:

Q: Show that the curve y = 2ex + 3x + 5x3 has no tangent line with slope 2.

A: To show that the slope of the tangent at every point is different form 2, for the given curve

Q: Find the point where the tangent line to y = 5x at x = 0.5 crosses the x-axis.

A:

Q: Show that the curve y = 6 x 3 + 5x -3            has no tangent line with slope 4.

A: y=6x3+5x-3 has no tangent line with slope 4

Q: Find the points on the curve y = 2x3 + 3x² – 12x + 5 where the tangent line is horizontal. (х, у) )…

A:

Q: 4. At what points on the curve y = 2x³ – 3x2 – 2x + 4 are tangents of slope 10?

A:

Q: What is the slope of the tangent line to the graph of x2-xy-4y2+2x+4y=8 at (4,-2)?

A: