2. If you will draw the graph of y = x(x+2)², how will you sketch it with respect to the x-axis? A. Sketch is crossing both (-2, 0) and (0, 0). B. Sketch is crossing (-2, 0) and is tangent at (0, 0). C. Sketch is tangent at (-2, 0) and crossing (0, 0). D. Sketch is tangent at both (-2, 0) and (0, 0).

Q: a Show that y = mx + b intersects y = |x + 1| if m > 1 or m < -1. b Given that -1 < m < 1, find the…

A: Given,y = mx + cFor m &gt; 1Take  m = 2 &gt; 1,

Q: A curve on the xy-plane passes through the point (0, a) for some number a, and has the property that…

A: This problem is based on a variable separable first order ordinary differential equation. We have to…

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

A:

Q: X = --6t-1 2 Find all points on the graph of that have either a vertical or horizontal y=- -9t +1 3…

A: Here given x=3t22-6t-1y=t33-9t+1

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)2 = 4(x- 5), (9, 7) %3D…

A:

Q: 7. An equation of the line tangent to the graph of ƒ at the point (2, 7)is y = 4x - 1. Find ƒ(2) and…

A: Given function is fxequation of the tangent line y=4x-1tangent of the graph 'f'=dfdx=y=4x-1  ∴…

Q: How will you sketch the graph of y =x (x-1)4 with respect to the x-axis? O A. sketch it tangent at…

A:

Q: 6. Find the point on the curve y = yx that is closest to the point (3, 0)

A: let P is the closest point then say (x,y) then find the distance from the point (3,0)  then minimize…

Q: 2.1 Identify and sketch the graph of y = /9 – 4x². Show all the necessary points on the curve and…

A: We can square the left-hand side and right-hand side then we get y2 = 9-4x2

Q: 28. The line tangent to the graph of g at the point (x, y) inter- sects the x-axis at the point…

A:

Q: The curve y = ax² + bx + c passes through the point (1,8) and is tangent to the line y= 6x at the…

A:

Q: 20. Find the point on the curve y= /x that is closest to the point (3, 0).

A:

Q: Assume y = 3 · 5* is the equation for the blue line shown in the graph below, and that the black…

A: The equation of curve is:  y=3·5x

Q: 10. Find the length of the curve y = x/2 + 8 on the interval [0, 2]

A:

Q: The curve y = ax2 + bx + c passes through the point (1, 2) and is tangent to the line y = x at the…

A:

Q: Find y' and the slope of the tangent line to the graph of (3x - 5y)5 = 2y2-9 at the point (3,2).…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the given…

Q: A line meets a curve y=2x-1 at the point (5,4). The line is tangent to the circde C:x +y² +10x+8y+…

A:

Q: 6. Find the length of the curve y =-+ from x =1 to x=2. 9. 28x

A: The curve is given by the equation, y=x99+128x7  and the point is given from x=1 to x=2. To find :…

Q: find the length of the curve on the given interval: y = 4/3 (x+1) ^ (3/2), [0,3]

A:

Q: Find a point on the graph of y = r where the tangent is parallel to the chord joining (1, 1) and (3,…

A:

Q: Grien that the graph of fx) passes throush the point (7,4) and that the slope of its tanger line at…

A: Given problem:- Given that the graph of f(x) passes through the point (7,4) and that the slope of…

Q: 11. What is the y-intercept of the line that is tangent to the graph of y =-x +4x at (1, 3)? a. -2…

A:

Q: Find the values of a and b for the curve x2y +ay? -b if the point (2, 2) is on its graph and the…

A: Given x2y+ay2=b

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

A: Given, The curve  y=ax3+bx2+12x-7 We have to find the value of a  and b such that tangent to the…

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A:

Q: The curve y = ax + bx +c passes through the point (1,4) and is tangent to the line y = 3x at the…

A:

Q: Find the point of inflection of the curve y = x^3 - 6x^2 - x+ 12. O (-2-6) O (2.6) O (2. -6) O…

A:

Q: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

A:

Q: Find an equation of the tangent to the curve at the given point. (1) X²+4xy-y²-4x=1, (1,2) (2)…

A:

Q: 9. Find the points on the graph y = 7x - where the slope of the tangent line is parallel to x-2 28x…

A: To find- Find the points on the graph y = 7xx - 2 where the slope of the tangent line is parallel to…

Q: 1. Find the slope of the given curve at the indicated point a. y = x³ – 4x? + 3, at x = 2 b. y =, at…

A:

Q: The tangent line to the graph of y = g(x) at the point (6, 4) passes through the point (2, 9). Find…

A: The tangent line to the graph y=g(x) at the point (6,4) passes through the point (2,9). Note:…

Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

A:

Q: 19. For what value of h will the line y =-2x +h be tangent to the parabola y = 3x +4x-1? (4T) b)…

A:

Q: The tangent line to the graph of y = g(x) at the point (9, 1) passes through the point (4, 6). Find…

A:

Q: Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a…

A: xy=C,  x2-y2=K Consider, xy=C Differentiating with respect to x, we get…

Q: Find the values of a and b for the curve x2 y + ay2= b if the point (1,1) is on its graph and the…

A: Find the slope of tangent line

Q: The equation of the tangent to the curve y = x – 3x² – 2x + 2 at the point where the curve cuts the…

A: We have to find  the equation of tangent in the form of y=mx+c.

Q: Consider the following graph. y y = arctan 2 (1) 4 -6 -4 -2 2 4 6 4 Given the function y = arctan…

A: For the solution of the problem follow the next step.

Q: Find the values of a and b for the curve x2y +ay2 = b if the point (2, 2) is on its graph and the…

A:

Q: For what value of c is the curve y = c/(x + 1)tangent to the line through the points (0, 3) and (5,…

A:

Q: Find y' and the slope of the tangent line to the graph of (3x - 4y)7 = 2y2-7 at the point (3,2).…

A: The slope of equation is defined in terms of m=dy/dx

Q: The tangent line to the graph of y = g(x) at the point (6, 8) passes through the point (3, 2). Find…

A:

Q: Suppose that dy xy + x d.x and that the point (5,0) lies on the graph of (x, y). What is the value…

A:

Q: Two different level curves of the graph of z = f(x, ygan intersect. O True False

A: The level curve of a function f of two variables are the curves with equations f(x ,y)= k, where k…

Q: 10. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

A:

Q: Choose the correct graph of y = sin x, - T < x < 2 T; and y = csc x, - T < X< 2T: 2 1 27 -1 -2

A:

Q: Consider the graph of (x^2) - (y^2/10) - (z^2/10) =1 1.What does the cross-section in the -plane…

A: The given equation represents a hyperboloid of two sheets.

Q: 6. Given the curve y = x/x at what point on the curve is the tangent parallel to the line 4x – y + 6…

A: We will use differentiation and slope of line to solve this.

Q: If you will draw the graph of y=x^2 (x-1), how will the graph behave at the x-axis?   A) The graph…

A: y= x2(x-1)at x = 0:y = 0(0-1)y = 0and at x=1, y=12 (1-1)Hence, The graph crosses (0, 0) and (1, 0).