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Find the value of x for which the function y = x³ – x has a minimum value…

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Find the value of x for which the function y = x³ – x has a minimum value

A. √3/3

B. √3

C. – √3/3

D. – √3

QUICK ANSWER…

A

DETAILS…

We would have to differentiate y = x³ – x and make x the subject of the formula.

dy/dx = 3x³ ¯ ¹ – 1x¹ ¯ ¹

dy/dx = 3x² – 1

the minimum value will the point at which dy/dx = 0

so, 3x² – 1 = 0

3x² = 1

x² = 1/3

x = √1/3

x = 1/√3

rationalizing,

x = 1/√3 × √3/√3

x = √3/3

Now for the right answer to the above question:

  1. Option A is correct.
  2. Option B is incorrect.
  3. C is not correct.
  4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

  • A function is minimum or maximum only at a point where dy/dx = 0.
  • So, for questions like this, you would have to firstly differentiate the function, and then equate the answer to 0.
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/ culled from 2020 JAMB-UTME mathematics past question 39 /

Find the value of x for which the function y = x³ - x has a minimum value... » QuizTablet
Find the value of x for which the function y = x³ - x has a minimum value... » QuizTablet

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