identify all x-values at which the graph of the function f (x) = 25x^4-70 x^3-26x^2+210x-147 has horizontal tangent line. round your answers to three decimal place.

x ∈ {-0.924, 1.400, 1.624}

Step-by-step explanation:

The local extrema of the function are nicely shown by a graphing calculator.

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If you like you can find the zeros of the derivative.

... f' (x) = 100x³ - 210x² - 52x + 210

By graphing or other means, you can determine that this has a zero at x=1.4, so can be factored as ...

... f' (x) = 2 (5x - 7) (10x² - 7x - 15)

The quadratic factor has roots at x = 0.35 ± √1.6225 ≈ {-0.924, 1.624}