What will be the point of minimum of the function 2x^3 + 3x^2 – 36x + 10?

(a) 1

(b) 2

(c) 3

(d) 4

This 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

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

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.