CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
The function f(x) = 2x³ − 9x² + 12x + 1 has its point of inflexion, where f''(x) = 0, at x equal to:
The point of inflexion is at x = 3/2. The second derivative is 12x − 18, which is zero at x = 1.5 and changes sign there. The values 1 and 2 are stationary points where the first derivative is zero.
- Ax = 1
- Bx = 2
- Cx = 3/2Correct
- Dx = 3
Explanation
f'(x) = 6x² − 18x + 12 and f''(x) = 12x − 18. Setting 12x − 18 = 0 gives x = 3/2. The values x = 1 and x = 2 are where f'(x) = 0 (stationary points), which is the key distractor.
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