Mathematics · JEE | APPLICATION OF DERIVATIVES
हिन्दीLet \( f(x) = x^3 - 6x^2 + 9x + 15 \). The point of local minima for this function is:
View Answer & Solution
Correct answer · Option A
\( x = 3 \)
Explanation
Derivative \( f'(x) = 3x^2 - 12x + 9 = 3(x-1)(x-3) = 0 \Rightarrow x = 1, 3 \). Second derivative \( f''(x) = 6x - 12 \). At \( x = 3 \), \( f''(3) = 6 > 0 \), hence it is a point of local minima.