Determine f'(x) for each of the following functions. (a) f(x) = x-x 6 (b) f(x) =...

  

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Determine f'(x) for each of the following functions. (a) f(x) = x-x 6 (b) f(x) = + 2-3 (5x7 +1) (x-2x) (d) f(x) = (1-x)4 (2x+6) 2. [15 Marks]. (a) Determine the slope of the tangent to f(x) = 2x(x + 1)5(x + 2x + 1) at x = -2. (b)Write the equation of the tangent line at x = -2. (c) Write the equation of the normal line at x = -2. (c) f(x) = 16 3. [4 marks]. Show that the line 4x -y + 11 = 0 is tangent to the curvey = 1/2-1. 4. [6 Marks]. Determine the point(s) where the tangent to the curve y = 2(x - 1)(5-x) is horizontal. 5. [6 marks]. Differentiate each function. (a) f(x) = (-44 (b) f(x) = x(1-x) (1+x) 6. [8 Marks]. Use the chain rule to find at the given value of x. dx (a) y = 2u + 3u, u = x + x at x = 1. (b) y=u-5(u - 7u),u = x, at x = 4. Determine f'(x) for each of the following functions. (a) f(x) = x-x 6 (b) f(x) = + 2-3 (5x7 +1) (x-2x) (d) f(x) = (1-x)4 (2x+6) 2. [15 Marks]. (a) Determine the slope of the tangent to f(x) = 2x(x + 1)5(x + 2x + 1) at x = -2. (b)Write the equation of the tangent line at x = -2. (c) Write the equation of the normal line at x = -2. (c) f(x) = 16 3. [4 marks]. Show that the line 4x -y + 11 = 0 is tangent to the curvey = 1/2-1. 4. [6 Marks]. Determine the point(s) where the tangent to the curve y = 2(x - 1)(5-x) is horizontal. 5. [6 marks]. Differentiate each function. (a) f(x) = (-44 (b) f(x) = x(1-x) (1+x) 6. [8 Marks]. Use the chain rule to find at the given value of x. dx (a) y = 2u + 3u, u = x + x at x = 1. (b) y=u-5(u - 7u),u = x, at x = 4.