A-LevelMathematicsDifferentiation9709/12 · Feb/Mar 2017 · Q78 Marks
The function f is defined for x ≥ 0 by f(x) = (4x + 1)³ᐟ².
- (i)Find f'(x) and f''(x).[3]
- (ii)The first, second and third terms of a geometric progression are respectively f(2), f'(2) and kf''(2). Find the value of the constant k.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.
- [B1B1] Expect 6(4x+1)^(1/2) but can be unsimplified. f'(x) = [3/2(4x+1)^(1/2)] [4]
- [B1] Expect 12(4x+1)^(-1/2) but can be unsimplified. Ft from their f'(x). f''(x) = 6 x 1/2 x (4x+1)^(-1/2) x 4
- [B1B1B1] f(2), f'(2), kf''(2) = 27, 18, 4k OR 12 Ft dependent on attempt at differentiation
- [M1A1] 27/18 = 18/4k oe OR kf''(2) = 12 ⇒ k = 3
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →