Given the equation of curves: y = x2 + 7x + 6 and x - 2y = 6. Find the slopes of the tangents of the curve drawn at the point of intersection?

Q: Find the equation of the line tangent to the curve y = 3x?(x² – 6x) at x = 2.

A:

Q: At what points does the equation of the line tangent to the curve y=1/x have a slope equal to −1?

A:

Q: Find the equation of the curve for which y"= 2x³. The slope of the inflectional tangent at (-1, 3)…

A:

Q: The curve's equation is given by x* + y4 = x² + y?

A: Here is the solution of the given problem.

Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: If y=mx+b is the equation of the tangent line the curve y = x- 3x +5, which is parallel to the…

A: We will solve the problem

Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

A:

Q: Find the slopes and equations of the lines tangent to y = f(x) at the given point.

A:

Q: A coordinate of the point on the curve of y=2x3−3x−6, where the tangent at the point is…

A:

Q: Find the coordinates of the points on the curve y = x³ - 6x² + 14x – 12 at which the tangents have a…

A: We will differentiate with respect to x and equate the same to 5 and find the points.

Q: The slope of the curve defined by the equation y-x + x =-2 at the point (-1,0) is %D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the length of the curve with equation x2 (y + 1)3 from the point where æ = 0 to the point where…

A: Since the given curve is  x2=y+13      from point x=0 to x=33. Given curve can be written as x=y+132…

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: Given the equation of curves: y = x2 + 7x + 6 and x - 2y = 6. Find the slopes of the tangents of the…

A: We begin by finding the points(s) of intersection of the 2 curves y =x2+7x+6  &  x-2y = 6y…

Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2…

A: Solution is here

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line.…

A: Given equation of a graph is 4x2+y2-8x+4y+4=0 Since we need to find the points where the tangent to…

Q: Find the slope and the equation of the tangent line to the curve and explain briefly.  y = 2x^2 –…

A: The slope of the curve at any point  x1,y1 can be calculated by using the formula m=dydxx1,y1 ,…

Q: find the slope of the curve at the point indicated y = 1/x - 1, x = 3

A:

Q: Find the equation of the tangents to the graph y = x^3 + 3x^2 - 15x -20 at Ox-y-9=0 O9x-y-48 = 0 O9y…

A:

Q: Find an equation of the line which is tangent to the circle r +y - dr + by – 12 = 0 at the point (5,…

A:

Q: For the curve y = ax3 + bx2 + 12x -7, what values of a and b will make the tangents to the curve at…

A: given  y=ax3+bx2+12x-7a=?b=?

Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

A:

Q: Given the curve y= x^3 - 4x +1 . Find the equation of the tangent at the points where the slope of…

A:

Q: The slope of the curve y = (5x² + 8x + e)eje at x = 0 is

A:

Q: s) Find the equation of the curve that passes through the point (3, 2) if its slope is giv dy = 8x –…

A:

Q: dy 20 yau

A:

Q: Given that y" = 2x, find the value of y when x = 3 if the curve passes through the point (-1,); and…

A:

Q: Show At what points does the equation of the line tangent to the curve y=1/x+3 have a slope equal to…

A:

Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: For the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: Given the curve y 2x-x, find the point(s) when the slope of the tangent line is 20.

A: Given the curve is  y=2x3-x2

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

Q: Find the slope of the tangent line to the curve - 6y3 – 42?y? = 2 at the point (1, – 1)

A: We have to find slope of the tangent line to the curve -6y3-4x2y2=2 at the point 1,-1

Q: Find the points on the curve where the tangent is vertical. x=1³-3t, y-t³-31²

A: First we find dy/dx

Q: If y=mx+b is the equation of the tangent line the curve y=x2-3x+5 , which is parallel to the secant…

A: Proceed as shown

Q: find the slope of the curve at the point indicated y = x - 1/x + 1, x = 0

A: Given, y=x-1x+1 and the point x = 0

Q: For a certain curve, y" = 6x – 8. Find its equation given that it passes through P(1, 0) with slope…

A:

Q: Find equations for the tangents to the circle (x - 2)2 + ( y - 1)2 = 5 at the points where the…

A:

Q: Find the equation of the tangent to the curve y 18x- 2y-3 0. 3e3 that is parallel to the line

A:

Q: Consider the curve that is given by the following equation 2/3 + y7/3 = 5 Determine the equation of…

A:

Q: find the slope of the curve at the point indicated. 19. у %3D 5x — Зх?, X =

A:

Q: Find an equation for the line that goes through the point (0,0) so that the tangent of the angle it…

A: Given, (x1,y1)= (0,0) tangent of the angle it makes with the x-axis=0

Q: Find the slope of the tangent line to the curve 2x + lay 4y 20 at the point (2,- 2).

A:

Q: , The equation y2(y? – 4) = x²(x² – 5) is known as the devil's curve. Give an equation for the…

A:

Q: The equation of the line that is tangent to the curve y=2x3−6x and is perpendicular to 18y+x+3=0…

A:

Q: Find the equations of the line tangent to the curve y = x³ + x , where the slope is equal to 4.

A:

Q: or the curve y = ax³ + bx² + 12x - 7, what values of a and b will make the tangents to the curve at

A: