Consider the following curve. y = 5 + 5x2 - 2x3. (a) Find the slope of the tangent to the curve at the point where x = a. m = (b) Find the equation of the tangent line at the point (1, 8). f(x) = (c) Find the equation of the tangent line at the point (2, 9). g(x) = Solution (a) slope dy/dx so 5.2.x-2.3 x^2 at x = a 10a-6a2 is the slope (b) y = mx + c m = 5.2.x-2.3 x^2 at x = 1 m = 4 y= 4x+ c at (1,8) c = 8-4= 4 so tangent is y = 4x + c (c) y=mx+c m at (2,9) is -4 y = -4x + c thro (2,9) c = 9+ 4. 2 = 17 so g(x) = y = -4x + 17.