# What are the points of inflection, if any, of #f(x)=x^4-5x^3+x^2 #?

The second derivative will be positive in the second case and negative in the first, meaning that the points of inflection are found at those points where the slope is changing from positive to negative (decreasing) or from negative to positive (increasing).

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To find the points of inflection, we first need to find the second derivative of the function.

f''(x) = 12x^2 - 30x + 2

Next, we find the values of x where f''(x) = 0.

12x^2 - 30x + 2 = 0

Solving this quadratic equation gives us the values of x.

x = (15 ± √109)/6

Therefore, the points of inflection are (15 + √109)/6 and (15 - √109)/6.

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