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3 years ago

Please solve this I need help.

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

8 0

<h3>I'll teach you how to solve |x-7|=x-7</h3>

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|x-7|=x-7

For each absolute find positive and negative intervals:

For x<7:

No solution

Merge overlapping intervals:

x $\geq$ 7

Your Answer Is x $\geq$ 7

plz mark me as brainliest :)

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Find the derivative of f(x) = 4 divided by x at x = 2.

polet [3.4K]

<h2>Hello!</h2>

The answer is:

$f'(2)=-1$

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

$f(x)=\frac{4}{x}$

It's a quotient, so, we need to use the following formula to derivate it:

$f'(x)=\frac{d}{dx}(\frac{u}{v}) =\frac{v*u'-u*v'}{v^{2} }$

Then, of the given function we have that:

$u=4\\v=x$

So, derivating we have:

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }$

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*0-4*1}{x^{2} }$

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }$

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }$

Hence,

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }$

Now, evaluating with x equal to 2, we have:

$f'(2)=\frac{-4}{(2)^{2} }$

$f'(2)=\frac{-4}{4}$

$f'(2)=-1$

Therefore, the answer is:

$f'(2)=-1$

Have a nice day!

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