61. Find the points on the graph of y2 = x³ – 3x +1 (Figure 10) where the tangent line is horizontal. (a) First show that 2yy' = 3x² – 3, where y' = dy/dx. (b) Do not solve for y'. Rather, set y' = 0 and solve for x. This yields two values of x where the slope may be zero. (c) Show that the positive value of x does not correspond to a point on the graph. (d) The negative value corresponds to the two points on the graph where the tangent line is horizontal. Find their coordinates. FIGURE 10 Graph of y² = x – 3x +1.

Q: What is the slope of the line tangent line to the curve x²y = y2 – 6x when x=2?

A: The given curve is x2y=y2-6x. Substitute x=2 in the above equation and obtain that,…

Q: Find the slope of the tangent to the parabola y=x^2 at x=1 a. 1 b. 2 c. 3 d.4

A: The slope pf the parabola = 2

Q: Find the slope of the tangent to the curve y = 3 + 4x² – 2x' at the point where x=a. Draw the graph…

A: Slope of the tangent is derivative of the function .

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: dy at(5, 4) for the following by implicit differentiation: dx x6 = 36 2. Find

A:

Q: Show that the tangent lines to the graph of y = (ex - e-x) / (ex + e-x) atx = 1 and x = -1 are…

A: Here we have to show that the tangent lines to the graph of y=ex-e-xex+e-x at  x=1 and x=-1 are…

Q: y' = 3√y + 6x³ 3

A:

Q: Find the slope of the tangent to the curve y=4/(5-4x) at x1=9

A:

Q: 9. Find the equation of the tangent line at point (2,2) on the curve fx) = x²- 7x + 12.

A: To find the equation of the tangent line

Q: Calculate y" and y'''.      y = ex /x

A: The given function is, y=exx Since the given expression is of the form y=fxgx, it can be…

Q: d Find {1+ 2x + 3x*} dx Find the equation of the tangent to y = 1++ 2x + 3x4 at the point with…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: 8. Find the equation of the horizontal tangent line to the curve y = -x + yx.

A: For horizontal  tangent line put the derivative  of function equals to zero

Q: 6. Let y + xy - y = 8x*. a) Find dy/dx using implicit differentiation. b) Find the equation of the…

A: In implicit differentiation, when we differentiate y, we use dy/dx