The point P(S, -2) lies on the curve y = 2/(4 - x). (a) If Q is the point (x, 2/(4 – x)), use your calculator to find the slope mag of the secant line PQ (correct to six decimal places) for the following values of x. (0 4.9 (i) 4.99 () 4.999 (iv) 4.9999 (v) 5.1 (vi) 5.01 (vii) 5.001

Q: Find the points on the curve y = x4- 6x2 + 4 where the tangent line is horizontal.

A: y=x4-6x2+4 Differentiating with respect to x, we get dydx=4x3-62x+0=4x3-12x Now the tangent line is…

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

A:

Q: Find the slope of the tangent to the curve at the point specified. x² +y² = 9 at (0, 3) The slope is

A:

Q: 4. Find the point on the curve y = 2x² – 12x + 5 where the tangent is horizontal.

A:

Q: At what point on the curve x = 3t2 + 5, y = t3 - 5 does the tangent line have slope ? (х, у) %3

A:

Q: At what point on the curve x 3t2 + 1, y = t3 - 5 does the tangent line have slope ? (х, у) -

A: We have given curve as x=3t2+1         ⋯⋯1y=t3-5           ⋯⋯2 From the equation (1) and (2), on…

Q: 12. Determine the y-intercept of a line with a slope of -2 that is a tangent to the curve: y =…

A:

Q: Find the slope of the tangent line to the curve g²y -y = 6 at the point (1, 3). -18/5 0. -3 18 -5/18

A:

Q: At which points on the curve y = 1 +°40x³ – 3x³ does the tangent line have the largest slope? | (x,…

A: Maximize slope

Q: What is the slope of the tangent line to the curve xy +y– 1=0 at the point (0, 1)? -1 -3 -2 1

A:

Q: Find the slope of the tangent line to the curve – 2a2 + xy + 4y³ = - 6 3 at the point (- 2, 1).

A:

Q: -1 Where on the curve y = (256+ x²)¯* does the tangent line have the greatest slope? NOTE: Enter the…

A:

Q: 7) Find an equation of the line tangent to the curve y = x+5 at x = 3. х-1

A:

Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: 1) Find the slope of the tangent lines on the curve y = 6x + 24x -39x - 43 at points | (-5,2) and…

A: Slope of line is given by m = dy/dx = tan θ y = 6x3 + 24x2 - 39x - 43  Differentiating with respect…

Q: Find the points on the curve y= x 4-6 x2 +4  where the tangent line is horizontal.

A: Find the points on the curve y=4x-6x2+4  where the tangent line is horizontal.

Q: Estimate the slope of the tangent to the curve y 0.25x at x = 2 algebraically by finding the slope…

A: We have to find the slope of the tangent to the curve at x=2 by finding the slope of the secant…

Q: Find the slope of the line tan gent to the curve of 2y³ + xy + 1 = 0 at the point (-3, 1) .

A:

Q: Find an equation of the tangent line to the curve at the given polnt. y = 4x² – x², (1, 3)…

A:

Q: At what point on the curve x = 6t2 + 5, y = t3 − 1 does the tangent line have slope of 1/2?

A: We can use application of derivative in order to solve the given problem.

Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

A:

Q: Find the slope of the tangent line to the curve defined by 4x + xy – y = 1760 at the point (8, –4).…

A:

Q: Find all points on the curve  x 2  y 2 + xy = 2  where the slope of the tangent line is - 1

A: We first find dy/dx using implicit differentiation

Q: -1 Where on the curve y = (196 + x²)¯ does the tangent line have the greatest slope? NOTE: Enter the…

A:

Q: Find an equation for the tangent line to the curve y = xV 2x² - 14 at the point (3,6). O y- 6 = 14(x…

A: The equation of the tangent line to the curve is, y - 6 = 11(x - 3)  The detailed solution is as…

Q: At what point on the curve x = 9t2 + 2, y = t3 - 6 does the tangent line have slope ? (x, y) = ])-

A: Consider the curve

Q: 8. Find the slope of the tangent of the curve x² + y² = 10 at the point (1, -3).

A:

Q: Find the slope of the tangent line to the curve V3x+y+v2ry = Vi+v4 at the point (2, 1). The slope is

A: To find the slope we need dy/dx

Q: 1. What is the slope of the tangent line to the curve 4x2 - 9y² = 1 at point (3,2) ? b. - 27 8 a. 3…

A:

Q: Find the equation of the tangent and normal line using the stipulated conditions   1.) y = x2 - 5x…

A: Given the equation is y = x2 - 5x The point of intersection line y=6 The equation of the tangent is…

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

A: The equation of the curve is given by y = 3+4x2-2x3 To evaluate: The slope of the tangent to the…

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: 2. At which points on the curve y = 1+ 60x – 2x does the tangent line have the largest slope?

A: Solution ) y = 1+60x3- 2x5 First derivative with respect to  x y' =0+ 60 ×3 × x2 - 2×5 x4 y' = 180x2…

Q: 4. The slope of the tangent line to the curve y 4. is: 9 - at the point 9, The equation of this…

A: To find the slope of the tangent line to the curve, y=4x, at the point 9, 49.The  equation of this…

Q: 2. What is the slope of the normal line to the curve 4x2 - 9y2 = 1 at point (3,2) ? a. 3 b. - 8. С.…

A: Normal at any point on the curve is a straight line that intersects the curve at that point and is…

Q: Find all the points on the curve x^2y^2+xy=2 where the slope of the tangent line is equal to -1

A:

Q: Find the equation of the line that is tangent to the curve y =-3e* at x = In 2. %3D

A:

Q: Find the slope of the tangent to the curve x° + 4xy+ y² = 13 at (1, 2). The slope is (Enter undef if…

A:

Q: -4 The number of tangents to the curve of y=- x³ + 6x? which have a slope of 8 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: What is the value of the slope of the tangent line to the curve x²+ 4.xy +y² =13 passing through the…

A: topic - slope of a tangent at a point on a curve

Q: What is the slope of the tangent line that touches the graph of In(y) + eA-=3y-4x at the point 3. 5

A:

Q: What is the slope of the tangent to the curve x-y² -x = - 4'at (1,2)

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

A:

Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

A:

Q: At which point on the curve y = 1 + 2e^x -3x is the tangent line parallel to the line 3x - y = 5…

A: The given curve is y = 1+2e^x-3x.In order to compute the slope of the tangent line of the curve,…

Q: 2 at the Find the equation of the tangent line to the graph y 3 (round the slope to one decimal…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.