Find the value of x for which the function y = x³ – x has a minimum value…
Find the value of x for which the function y = x³ – x has a minimum value
C. – √3/3
D. – √3
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
x = 1/√3 × √3/√3
x = √3/3
Now for the right answer to the above question:
- Option A is correct.
- Option B is incorrect.
- C is not correct.
- D is not the correct answer.
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
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