Question

If M be the greatest value and m be the least value of

ƒ(x) = 2x³ – 3x² – 12x + 1, for –1 £ x £ 3/2, then the ordered pair (M, m) is –

• A. (8, –19)
• B. (8, – 17)
• C. (–17, –19)
• D. None

Answer 1

Answer: (B)

(8, – 17)

Answer 2

ƒ(x) = 2x³ – 3x² – 12x + 1

ƒ¢(x) = 6(x² – x – 2) = 0 for x = –1, x = 2

But x = 2 is outside the interval [–1, 3/2] :

for –1 < x < 3/2 ; ƒ¢(x) < 0.

f(x) is decreasing.

M = ƒ(–1) = –2 – 3 + 12 + 1 = 8; m = f(3/2) = –17.