Name: ................................................... 10A Date: ................................................... INSTRUCTIONS • You should use a calculator where appropriate. • You must show ALL necessary WORKING/SOLUTION clearly. T3 CA 3 TOTAL MARKS: 40 1. 𝑦 = 3𝑥 2 − 12𝑥 + 7 a. Find the value of 𝑑𝑦 𝑑𝑥 when 𝑥 = 5. ……………………………… [ ___ /3] b. Find the coordinates of the point on the graph of 𝑦 = 3𝑥 2 − 12𝑥 + 7 where the gradient is 0. ( .................... , .................... ) [ ___ /2] 2. A curve has equation 𝑦 = 𝑥 3 − 𝑎𝑥 + 𝑏. The stationary points of the curve have coordinates (2, 𝑘) and (−2, 10 − 𝑘). Work out the value of a, the value of b, and the value of k. a = .............................. , b = .............................. , k = .............................. [ ___ /6] 3. The curve with the equation 𝑦 = 3𝑥 2 − 12𝑥 + 7 is plotted and a tangent with gradient −8 is drawn on the curve. a. Find the coordinates of the point where the tangent meets the curve. ( .................... , .................... ) [ ___ /4] b. What is the equation of the tangent? ……………………………… [ ___ /3] 4. The equation of a curve is 𝑦 = 4𝑥 3 − 3𝑥. Determine: a. the coordinates of the turning point. ( .................... , .................... ) and ( .................... , .................... ) [ ___ /5] b. the equation of the tangent to the curve at the point where x = 1. ……………………………… [ ___ /5] c. maxima and minima for this function. Give reasons for your answers. [ ___ /3] 5. The equation of a curve is 𝑦 = 5 − 3𝑥 − 2𝑥 4 . Find 𝑓′′(𝑥) . ……………………………… [ ___ /3] 6. The tangent to the curve 𝑦 = 5𝑥 − 2𝑥 2 at the point (2, 2) meets the 𝑦 − 𝑎𝑥𝑖𝑠 at point P. Find the coordinates of P. ( .................... , .................... ) [ ___ /6]