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What will be the point of minimum of the function 2x^3 + 3x^2 – 36x + 10?(a) 1(b) 2(c) 3(d) 4This question was posed to me during an interview for a job.This interesting question is from Calculus Application in division Application of Calculus of Mathematics – Class 12

Answer»

Right answer is (b) 2

For explanation I WOULD say: Let y = 2x^3 + 3x^2 – 36x + 10……….(1)

Differentiating both sides of (1) with respect to x we get,

dy/dx = 6x^2 + 6x – 36

And d^2y/dx^2 = 12x + 6

For MAXIMA or minima value of y, we have,

dy/dx = 0

Or 6x^2 + 6x – 36 = 0

Or x^2 + x – 6 = 0

Or (x + 3)(x – 2) = 0

Therefore, EITHER x + 3 = 0 i.e., x = -3 or x – 2 = 0 i.e., x = 2

Now, d^2y/dx^2 = 12x + 6 = 12(2) + 6 = 30, which is > 0.


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