Please complete the following questions:

5. a) Find the slope of the tangent lines to the parabola y = x3 + 6x 'i" at the points whose x-eoordinates are given 1) -5 ii) -3 iii) t) h) Graph the parabola and the three tangent lines. ti. a) Find the slope of the tangent line to the parabola y = x2 + x + 1 at the general point whose .r-coordlnate is a. h) Find the slope of the tangent lines at the points whose xcoordinates are (i) 1, {ii} E and (iii) 1. T. 3.) Find the slope of the tangent line to the parabola y = 2x2 x + 3 at the general point whose x-coordinate is a. h) At what point on the parabola does the tangent have a slope of 7'? 8. Find the points of intersection of the parabolas y = xz and y = 1 ix? Show that at each of these points the tangent lines to the two parabolas are perpendicular. 9. 21) Find the slope of the tangent line to the parabola y = x2 at the general point whose .r-coordlnate is a. 1)) Determine the equation of the tangent(s) to the parabola y = x2 passing through the point (U, Q). 10. Let (a. b) be a point on the graph of y = i Prove that the area of the triangle formed by the tangent through (a, b}, the xaxis and the y-axis has an area of 2. 1. For each of the following curves a) Find the slope of the tangent at the given point, b) Find an equation of the tangent at the given point, c) Graph the curve and the tangent. i) y = 3 -xz at (1, 2) ii) y = x + 2x - 1 at (2, 3) iii) y = 1 - x3 at (0, 1) 2. For each of the following curves a) Find the slope of the tangent at the given point, b) Find an equation of the tangent at the given point, c) Graph the curve and the tangent. i) y = - at (2, 1) x+5 ii) y = x-2 at (3, 8) x-3 iii) y = 2-3 at (-2, -5) 3. For each of the following curves a) Find the slope of the tangent at the given point, b) Find an equation of the tangent at the given point, c) Graph the curve and the tangent. i) y = vx + 2 at (7, 3) ii) y = vx2 + 3x at (1, 2) ili) y = at (1, 1) 4. Find the equation of the tangent line to the curve at the given point. a) y = 1+ 2x - x2, (1, 2) b) y = v2x + 1, (4, 3) 2x c) y = +1' (1, 1)