Question

What are the points of inflection of #f(x)= x^3 - 12x^2 + 2x + 15x #?

Answer 1

`"(4 , -30)"` is the inflection point.

Explanation:

Determining the points of inflection is by finding the second
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derivative then solve the equation for `f''(x)=0`.
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`f'(x) = 3x^2 - 24x + 2 + 15`
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`f''(x) = 6x -24`
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`f''(x) = 0`
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`6x -24 = 0`
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`rArr 6x = 24`
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`rArr x = 24/6 = 4`
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Finding its ordinate `f(4)`.
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`f(4) = 4^3 - 12(4)^2 + 2(4) + 15(4)`
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`f(4) = 64 - 192 + 8 + 90`
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`f(4) = -30`
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Hence, `"(4 , -30)"` is the inflection point.