If y = a ln | x + 1 | + b (x + 1)2 + x has its extremum valu... | MATH - MAXIMA AND MINIMA | SolveeIt | Solveeit

Today, August 20

Question

If y = a ln | x + 1 | + b (x + 1)² + x has its extremum value 4 at x = 0, then (a, b) is –

A

(– 9, 4)

B

(9, – 4)

C

(5, – 4)

D

(5, 4)

Answer

(– 9, 4)

Explanation

Solution

y = a log |x + 1| + b (x + 1)² + x

at x = 0, y = 4

4 = a log |1| + b ̃ b = 4

$\frac{dy}{dx}$ = $\frac{a}{x + 1}$ + 2b (x + 1) + 1

$\left( \frac{dy}{dx} \right)_{x = 0}$ = a + 2b + 1 = 0 ̃ a + 2 × 4 + 1 = 0

a = –9 ̃ (a, b) ̃ (–9, 4)