What is the nature of the function f(x) = 2/3(x^3) – 6x^2 + 20x – 5?(a) Possess only minimum value(b) Possess only maximum value(c) Does not possess a maximum or minimum value(d) DatainadequateThis question was addressed to me during an online interview.Asked question is from Calculus Application topic in division Application of Calculus of Mathematics – Class 12

What is the nature of the function f(x) = 2/3(x^3) – 6x^2 + 20x –

1.	What is the nature of the function f(x) = 2/3(x^3) – 6x^2 + 20x – 5?(a) Possess only minimum value(b) Possess only maximum value(c) Does not possess a maximum or minimum value(d) DatainadequateThis question was addressed to me during an online interview.Asked question is from Calculus Application topic in division Application of Calculus of Mathematics – Class 12
Answer» Right choice is (c) Does not possess a maximum or minimum value Easiest EXPLANATION: We have, f(x) = 2/3(x^3) – 6x^2 + 20x – 5 ……….(1) DIFFERENTIATING both side of (1) with RESPECT to x, we get, f’(x) = 2X^2 – 12x + 20 Now, for a maximum and minimum value of f(x) we have, f’(x) = 0 Or 2x^2 – 12x + 20 = 0 Or x^2 – 6x + 10= 0 So, x = [6 ± √(36 – 4*10)]/2 x = (6 ± √-4)/2, which is imaginary. Hence, f’(x) does not vanishes at any point of x. Thus, f(x) does not possess a maximum or minimum value.

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