# What are the points of inflection, if any, of #f(x)= -14x^3 + 19x^2 - x - 2 #?

Points of inflection are

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To find the points of inflection, we first need to find the second derivative of the function and then solve for where the second derivative equals zero. The second derivative of ( f(x) = -14x^3 + 19x^2 - x - 2 ) is ( f''(x) = -84x + 38 ). Setting ( f''(x) = 0 ) and solving for ( x ), we get:

[ -84x + 38 = 0 ] [ -84x = -38 ] [ x = \frac{38}{84} = \frac{19}{42} ]

Thus, the point of inflection of the function ( f(x) ) is ( \left(\frac{19}{42}, f\left(\frac{19}{42}\right)\right) ).

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