Question #f36b9

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Question #f36b9

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Answer 1 · 2018-01-25T05:47:05

Refer explanation.

Explanation:

Given -

$y = x^{4} + 8 x^{3}$ $y=x^4+8x^3$

To graph, a function, first find the turning points.
Find the first derivative and set it to zero, so that you know the value of $x$ $x$ , the slope of the curve becomes zero.

$\frac{d y}{d x} = 4 x^{3} + 24 x^{2}$ $dy/dx=4x^3+24x^2$

$\frac{d y}{d x} = 0 \Rightarrow 4 x^{3} + 24 x^{2} = 0$ $dy/dx=0=>4x^3+24x^2=0$

$4 x^{2} (x + 6) = 0$ $4x^2(x+6)=0$

$4 x^{2} = 0$ $4x^2=0$

$x = 0$ $x=0$

$x = - 6$ $x=-6$

At $x = 0$ $x=0$ and at $x = - 6$ $x=-6$ , there are turning points.
Take a range of values that includes 0 and -6. Calculate the corresponding value of $y$ $y$ . Tabulate them. Use the pair of the points to obtain the curve.

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At $x = 0$ $x=0$ , there is a point of inflexion.
At $x = - 8$ $x=-8$ , the curve reaches the minimum.

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Question #f36b9

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