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

Category: QuestionsWhat will be the point of minimum of the function 2x^3 + 3x^2 – 36x + 10?
Editor">Editor Staff asked 11 months ago

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

(a) 1

(b) 2

(c) 3

(d) 4

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This interesting question is from Calculus Application in division Application of Calculus of Mathematics – Class 12
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Editor">Editor Staff answered 11 months ago

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.