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SIZIF [17.4K]
3 years ago
10

The minimum value of the slope of the curve y=x^5+x^3−2x is: A. 0

Mathematics
1 answer:
patriot [66]3 years ago
6 0
The given curve is --- y = x^5 + x^3 - 2x 

<span>First derivative to this curve is y' = 5 x^4 + 3 x^2 - 2 </span>

<span>=> Slope (m) = 5 x^4 + 3 x^2 - 2 </span>

<span>For the minimum value of m we calculate dm/dx and put it = 0 </span>

<span>=> d( 5 x^4 + 3 x^2 - 2 ) / dx = 0 </span>

<span>=> 20 x^2 + 6 x = 0 </span>

<span>=> x ( 20 x + 6 ) = 0 </span>

<span>Turning values of x are 0 and - 6 / 20 = ( - 3 / 10 ) </span>

<span>At x = 0 , m = - 2 </span>

<span>and at x = - 3/10 </span>

<span>m = 5 x^4 + 3 x^2 - 2 </span>

<span>=> m = 5 ( - 3 / 10 )^4 + 3 ( - 3 / 10 )^2 - 2 = - 1.68 </span>

<span>Hence at turning points, the slope is minimum at x = 0 and is equal to = - 2 </span>

<span>MINIMUM VALUE OF THE SLOPE = - 2</span>
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