Date | May 2014 | Marks available | 3 | Reference code | 14M.1.sl.TZ1.10 |
Level | SL only | Paper | 1 | Time zone | TZ1 |
Command term | Find | Question number | 10 | Adapted from | N/A |
Question
Let f(x)=x4.
Write down f′(x).
Point P(2,6) lies on the graph of f.
Find the gradient of the tangent to the graph of y=f(x) at P.
Point P(2,16) lies on the graph of f.
Find the equation of the normal to the graph at P. Give your answer in the form ax+by+d=0, where a, b and d are integers.
Markscheme
(f′(x)=) 4x3 (A1) (C1)
[1 mark]
4×23 (M1)
Note: Award (M1) for substituting 2 into their derivative.
=32 (A1)(ft) (C2)
Note: Follow through from their part (a).
[2 marks]
y−16=−132(x−2) or y=−132x+25716 (M1)(M1)
Note: Award (M1) for their gradient of the normal seen, (M1) for point substituted into equation of a straight line in only x and y (with any constant ‘c’ eliminated).
x+32y−514=0 or any integer multiple (A1)(ft) (C3)
Note: Follow through from their part (b).
[3 marks]