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3 years ago

Solve: 6 -x= 4(5 + x)- 4

Mathematics

1 answer:

Serggg [28]3 years ago

7 0

Answer:

x = - 2

Step-by-step explanation:

Given

6 - x = 4(5 + x) - 4 ← distribute and simplify right side

6 - x = 20 + 4x - 4

6 - x = 16 + 4x ( subtract 4x from both sides )

6 - 5x = 16 ( subtract 6 from both sides )

- 5x = 10 ( divide both sides by - 5 )

x = - 2

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Answer:

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Local maximum

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Step-by-step explanation:

Let be $g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}$ . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:

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Then, first and second derivatives of the function are, respectively:

First derivative

$g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)$

$g'(x) = 2\cdot x^{3}-10\cdot x^{2}-28\cdot x +2\cdot x^{3}-5\cdot x^{2}$

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$g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)$

Second derivative

$g''(x) = 12\cdot x^{2}-30\cdot x -28$

Now, let equalize the first derivative to solve and solve the resulting equation:

$x\cdot (4\cdot x^{2}-15\cdot x -28) = 0$

The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:

$x\cdot (x-5.118)\cdot (x+1.368) = 0$