Question

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.

Answer 1

x ∈ {-0.924, 1.400, 1.624}

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}