Refer to the graph of y=f(x)=x2+x shown. ​a) Find the slope of the secant line joining (2, f(2)) and (4, f(4)). ​b) Find the slope of the secant line joining (2, f(2)) and (2+h, f(2+h)). ​c) Find the slope of the graph at (2, f(2)). ​d) Find the equation of the tangent line to the graph at (2, f(2)).

Q: the sloper of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

A: 1) Find dydx at the given points to find the value of 'a' . 2) Now satisfy the point (1,-1) to the…

Q: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

A:

Q: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

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

A:

Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

A:

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

Q: What is the slope of the secant line that passes through the points(a, f(a)) and (b, f(b)) on the…

A: Given: The secant line passes through the points a,fa  and  b,fb. Concept used: The slope of a line…

Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: Graph the relation of equation x2/4 + y2/16 = 1 using the points calculated in the table below.…

A: Answer

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: What are the coordinates of the points in the graph of y-x+6x-13=0 in which the tangent line is…

A: Given query is to find the point where tangent line is horizontal.

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: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ?

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: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…

A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A:

Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: Find the equation of the family of curve whose slope at any point (x,y) is (x+1)/(y-1)

A:

Q: Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes…

A:

Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

A:

Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A: To find the points at which tangent line is horizontal , y' =0.

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: 1. Find the DE of all straight lines with slope and y-intercept equal.

A:

Q: The point (0, 1) has the distance from the line defined by y = -2x – 1

A: Solve for distance

Q: Find the member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

A:

Q: Graph the relation of equation x2/4 + y2/16 = 1 using the points calculated in the table below.…

A: We have to graph the function x24+y216=1 by using the points in the table.

Q: B) Find the equations of all lines having slope-1 that are tangent to the curve y = -3)

A:

Q: End the Vellue of g) if the slope of the Curve y= x-2x is (2)?

A:

Q: what point/s (x,y) on the graph of f has/have the property that the line tangent to f at (x,y) has…

A:

Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: a. The curve y=4x-x and the lines y=0, x=1 and x=3.

A: Due to our guidelines we can answer only one question at a time, therefore I am answering first…

Q: What is the slope of the secant line that intersects the graph of h(x) = 16 – z at z = l and a = 4?

A: The slope of the secant line or any other line can be defined as the rise to the run ratio which is…

Q: Find an equation of the curve that passes through the point (1, −2), and has the given slope y′ =…

A:

Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: Find the slope of the line normal to the curve y x3 – 2x + 1 at x = 2

A: Our Aim is to find the slope of the line normal to the curve y=x3-2x+1-(i) at x=2.

Q: Find the equation of a line normal to the curve x^2=16y at (4,2).

A: Solve the given problem.

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

A:

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: Find the equation of the family of curves whose slope at any point (x,y) is   2. x/y

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

A: To find the equation of family of curves whose slope is given .

Q: What is the slope of AC in right triangle ABC shown in the standard (x, y) coordinate plane above?

A: Given,         A right triangle ABC is shown below :