The point P(7, 1) lies on the curve y = Vx - 6. (a) If Q is the point (x, Vx - 6), use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.5 (ii) 6.9 (iii) 6.99 (iv) 6.999 (v) 7.5 (vi) 7.1 (vii) 7.01

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

A:

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

A:

Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x -4 and parallel to the line 6x…

A:

Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of y…

A: y''' = 6 Implies, y" = 6x + a, where, a is a constant. &, y' = 3x² + ax + b, where, b is a…

Q: At which points on the curve y = 1 + 40 x3  - 3 x 5  does thetangent line have the largest slope?

A: The given equation of the curve is y=1+40x3-3x5. The slope of this given curve is given by its…

Q: Find the slope of the curve x2 + y3 = 2 at each point wherey = 1

A:

Q: What is the slope of the line tangent to the curve defined by y +xy-x 11 at the point (2, 3)

A:

Q: 8. The line y = -4x + b is tangent to the curve f(x) = 2x² – 8x + 12. Determine the value of b. %3D

A: The equation of the tangent at a point h,k on a curve y=f(x) is given by, y-k=f'(h) (x-h)

Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

A:

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: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

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

A:

Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: Find the equation of the curve that passes through the point (0, 2) and has a slope of at any point…

A:

Q: the equation of the tange

A: Given that: The equation of the curve x2 + 4y2 = 8. The equation of the line x + 2y = 8.

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 curve y=x4 at x=3.

A: Find the slope of the curve y=x4  at    x=3.

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

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: 4. Find the equation of the curve for which y""= 2x³. The slope of the inflectional tangent at (-1,…

A:

Q: Determine slope of a curve y = x³3 + 1 at x = 1

A:

Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: Find the eqaution of the curve that passes through (0,1) if its slope is given by y'=1/2X at any…

A:

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: 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 x-coordinate of the point where the curve y = x3 - x crosses the horizontal line y = 1.

A: Given:                                 y=x3-x and y=1  Let                                y=x3-x…

Q: (5) Find all the points on the curve y = 1/x where the tangent line is perpendicular to the line y =…

A:

Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x

A:

Q: 2. Find the equation of the tangent line to the curve y = x³+ 2x² – x at the point (-2, 7).

A:

Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

A:

Q: Find equations of all lines having slope -1 that are tangent to the curve y = 1/(x - 1).

A: Given, y=1x-1 Slope,m=-1

Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: B. Find the slope of the curve at the point indicated. 1. y = at x = -1 4-x2 %3D 2x+3 2. y = xv1 +…

A:

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

A:

Q: At which points on the curve y =1 +40x3  -3x5 does thetangent line have the largest slope?

A:

Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

A:

Q: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

A:

Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x - 4 and parallel to the line 6x…

A:

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangent…

A: To find the x-intercept we plug y=0

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

A: x2-xy+y2=36

Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

A:

Q: 15.)) What is the slope of the line tangent to the curve y +2 = - 2sin y at the point (2, 0)? 2 (A)…

A:

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A:

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

A:

Q: Find the slope of the tangent line to the curve defined by 9a – 8zy – y* = -18 at the point (-1,…

A:

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

A: