Part A: Solve the equation 7x + 3x − 18 = 6(x + 3), and show your work. (5 points)
2 answers:
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The second derivative at the point (2,2) is 34/9
<u>Explanation:</u>
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2x⁴ = 4y³
2x⁴ - 4y³ = 0
We first need to find dy/dx and then d²y/dx²
On differentiating the equation in terms of x
dy/dx = d(2x⁴ - 4y³) / dx
We get,
dy/dx = 2x³/3y²
On differentiating dy/dx we get,
d²y/dx² = 2x²/y² + 8x⁶/9y⁵
d²y/dx² = 34/9
Therefore, the second derivative at the point (2,2) is 34/9
<span>For this case we have the following expression:
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<span> We are going to make the following change of variables:
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<span>Rewriting the expression we have:
</span>
<span>Factoring the expression we have:
</span>
<span>Canceling similar terms we have:
</span>
<span>Returning the change we have:
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<span> The resctrictions of the function are those that make the denominator equal to zero.
We have then:
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<span> Answer:
The simplified expression is:
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<span>The restrictions are:
</span>
</span>
<span> We are going to make the following change of variables:
</span>
<span>Rewriting the expression we have:
</span>
<span>Factoring the expression we have:
</span>
<span>Canceling similar terms we have:
</span>
<span>Returning the change we have:
</span>
<span> The resctrictions of the function are those that make the denominator equal to zero.
We have then:
</span>
<span> Answer:
The simplified expression is:
</span>
<span>The restrictions are:
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