(a) Find the slope of the tangent line to the curve at the point (1, 0). (b) Find an equation of the tangent line in part (a). y = (c) Graph the curve and the tangent line. y y 4 2 2 -2 -2 -2 -2 2. 2. 2.
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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.Find the slope m of the tangent to the curve y = 8 + 4x2 − 2x3 at the point where x = a. (b) Find equations of the tangent lines at the points (1, 10) and (2, 8). y(x) = (at the point (1, 10)) y(x) = (at the point (2, 8))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 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 pointequation of the line tangent to the curveThe slope of the curve y^2-xy-3x=1 at the point (0,-1)
- 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.A) Find the slope m of the tangent to the curve y = 9+4x^2-2x^3 at point where x = a. B) Find equation of the tangent line at the point (1, 11) C) Find equation of the tangent line at the point (2, 9)equation of the tangent line to the curve at the given point. y = 2 + x3 , (−1, 1)
- a)Find an equation of the line tangent to the graph of y = x2 + 1 at the point (2, 5)b) Find an equation of the line perpendicular to the graph of y = x2 + 1 at (2, 5)c) Where is the line tangent to the graph of y = x2 + 1 horizontalFind 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) Find the slope of the tangent line to the curve y = x - x3 at the point (1, 0)(i) using Definition 2 (ii) using Equation 3(b) Find an equation of the tangent line in part (a).(c) Graph the curve and the tangent line in successively smaller viewing rectangles centered at (1, 0) until the curve and the line appear to coincide.