What is the maximum slope of the curve $y = - x^{3} + 3 x^{2} + 2 x - 27 ?$

2

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5

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21

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12

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Solution

The correct option is B $5$
Given curve $y = - x^{3} + 3 x^{2} + 2 x - 27$
$\frac{d y}{d x} = - 3 x^{2} + 6 x + 2$
Slope $m = - 3 x^{2} + 6 x + 2$
Now, $\frac{d m}{d x} = - 6 x + 6$
For maximum or minimum,
$\frac{d m}{d x} = 0$
$\Rightarrow x = 1$
Now, $\frac{d^{2} m}{d x^{2}} = - 6 < 0$ at $x = 1$
Hence, $m$ has a maximum at $x = 1$
Maximum value $= - 23$

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Similar questions

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^{'} a^{'}

A (x, y)

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