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Finding Equations of Tangent Lines:- Consider the equation x4 = 4(4x2 - y2).
Find and graph the four tangent lines to the curve for y =3.
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- Find equations for the horizontal tangent lines to the curve y = x3 - 3x - 2. Also find equations for the lines that are perpendicular to these tangent lines at the points of tangency.a. Find an equation for the line that is tangent to the curve y = x3 - x at the point (-1, 0). b. Graph the curve and tangent line together. The tangent intersects the curve at another point. Use Zoom and Trace to estimate the point’s coordinates. c. Confirm your estimates of the coordinates of the second intersection point by solving the equations for the curve and tangent line simultaneously.Find equations of the tangent lines to the curve y=(5ln(x)) / x at the points (1,0) and (e, 5/e) at the point (1,0) y= at the point (e, 5/e) y= Illustrate by graphing the curve and its tangent lines.
- a. Find an equation for the line that is tangent to the curve y = x3 - 6x2 + 5x at the origin. b. Graph the curve and tangent line together. The tangent intersects the curve at another point. Use Zoom and Trace to estimate the point’s coordinates. c. Confirm your estimates of the coordinates of the second intersection point by solving the equations for the curve and tangent line simultaneously.a.Find equations for the horizontal tangent lines to the curve y = x3 - 3x - 2. Also find equations for the lines that are perpendicular to these tangent lines at the points of tangency. b. Smallest slope What is the smallest slope on the curve? At what point on the curve does the curve have this slope? Find an equation for the line that is perpendicular to the curve’s tangent line at this pointA straight line from the origin passes through the point P(x, y) in the first quadrant and is inclined at θ = π 3 from the positive x-axis. Write an equation for the line.
- Find the slope and equation of the tangent line to the graph of the equation at a given point. Show your solution. 1. y = 2x² + 4x at point (-2,0)A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this point of contact. Write an equation in point-slope form for the line tangent to the circle whose equation is x2 + y2 = 25 at the point (3, -4).Please show complete solution and explanation. DETERMINE THE SLOPE OF THE TANGENT LINE TO THE CURVE y=2 – x2 at the point (3,-7)
- Tangent lines Find an equation of the line tangent to the following curves at the given point. y2 = 8x; (8, -8)Calculating the length of the curve segment given by equationUsing the implicit derivation method: If x2 + y2 = 25, find the slope of the equation of the line tangent to the curve at the point (3,4).