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Answer 1 · 2017-12-27T10:11:48

$\frac{d y}{d x} = x^{2} - 6 x + 5$ $dy/dx = x^2 - 6x + 5$

$\frac{d y}{d x} = 0$ $dy/dx = 0$ when $x^{2} - 6 x + 5 = 0$ $x^2 - 6x + 5 = 0$

or, $(x - 1) (x - 5) = 0$ $(x - 1)(x - 5) = 0$

i.e. the gradient is zero at $x = 1$ $x = 1$ and at $x = 5$ $x = 5$

Using iterative methods on $y = \frac{x^{3}}{3} - 3 x^{2} + 5 x + 7$ $y=(x^3)/3 -3x^2 +5x + 7$ we get,

$x \approx - 0.88$ $x~~-0.88$ , $x \approx 4.12$ $x~~4.12$ and $x \approx 5.77$ $x~~5.77$

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