# What are the points of inflection, if any, of #f(x)=2x^3 -10x^2 +3 #?

Point of inflection:

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To find the points of inflection of ( f(x) = 2x^3 - 10x^2 + 3 ), we need to find the second derivative, ( f''(x) ), and then solve for ( x ) when ( f''(x) = 0 ).

First, find the first derivative: [ f'(x) = 6x^2 - 20x ]

Next, find the second derivative: [ f''(x) = 12x - 20 ]

Set ( f''(x) ) equal to zero and solve for ( x ): [ 12x - 20 = 0 ] [ 12x = 20 ] [ x = \frac{20}{12} = \frac{5}{3} ]

Therefore, the point of inflection of ( f(x) ) is ( x = \frac{5}{3} ).

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