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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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I am really confused about this question for math.. any help would be really appreciated:
Elina [12.6K]

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A reflection about the x axis, about y=0, is the mapping (x',y')=(x,-y) so

y'= -y = - (\frac 1 4)^{x'}

A dilation of 2 is the mapping (x'',y'')=(2x', 2y')

So

x'=x''/2, y'=y''/2

y''/2= - (\frac 1 4)^{x''/2}

y'' =  - 2((\frac 1 4)^{1/2})^{x''}

y''= - 2(\frac 1 2)^{x''}

We can rewrite that without the primes and combine the powers of 2.

y =  - 2^{1-x}

Let's graph these and see if we're close,

Plot y= (1/4)^x, y= - (1/4)^{x}, y = - 2^{1-x}

6 0
3 years ago
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kherson [118]

Answer:

X=11º

Y=26º

Step-by-step explanation:

77=7x      11=x

180=77+77+y        26=y

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2 years ago
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aleksandr82 [10.1K]
Ngl I think it’s 20 because 15 is 5x3 but 60 divided by 3=20 lmk if I’m wrong
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Are you cyclist travels at a rate of 1.8 km/min. how far will the cycle is travel in 48 minutes
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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