Help needed with f' equation

[meano]

Can somebody walk me through this please

Question is - given the equation f (x) = (2x + 4) / sqrt x evaluate:

1, f (0.5)
2 , f' (0.5)

For 1 I get the answer 7.07 but struggling with 2.

Thanks

 

[stapel]

Question is - given the equation f (x) = (2x + 4) / sqrt x evaluate:

1, f (0.5)
2 , f' (0.5)

For 1 I get the answer 7.07...

Do the instructions specify that you're supposed to express the value as a decimal approximation rather than in exact form?

...but struggling with 2.

Can you find the derivative of 2x + 4? Can you find the derivative of the square root of x? Have you heard of the Quotient Rule yet?

Thank you!

 

[meano]

No they don't state how to express the value, that is just the answer I got. How would you express it in its exact form? Not sure what you mean there. This is an engineering course I am doing, we have been told we don't really need to fully understand this section but I want to so I am asking for help to explain it.

Sqrt x=

= x^1/2

= 1/2 x^(1/2-1)

= x^-1/2

= 1/2 Sqrt x

I think thats it.

Thanks!

 

[stapel]

How would you express it in its exact form?

Don't plug the result into your calculator. Instead of doing the extra step to get the decimal approximation, stop with what you got when you plugged "1/2" in for x (after you simplified, of course), just like you did back in algebra.

. . . . .\(\displaystyle f\left(\dfrac{1}{2}\right)\, =\, \dfrac{2\left(\frac{1}{2}\right)\, +\, 4}{\sqrt{\frac{1}{2}\,}}\, =\, \dfrac{1\, +\, 4}{\frac{1}{\sqrt{2\,}}}\, =\, \left(\dfrac{5}{1}\right)\,\left(\dfrac{\sqrt{2\,}}{1}\right)\)

...and so forth.

Sqrt x=

= x^1/2

= 1/2 x^(1/2-1)

I will guess that the above is meant to say the following:

. . . . .\(\displaystyle y\, =\, \sqrt{x\,}\, =\, x^{\frac{1}{2}}\)

. . . . .\(\displaystyle y'\, =\, \left(\dfrac{1}{2}\right)\,x^{\frac{1}{2}-1}\)

Generally, a function does not equal its derivative. In this particular case, the square root of x does not equal 1/(2sqrt[x]).

I will guess that you are familiar with how to differentiate 2x + 4. Since you don't mention or demonstrate the Quotient Rule, I will guess that you haven't covered that (though I have no idea how you're expected to do this without that Rule). Since we cannot teach courses here, please try online resources, such as are listed here.

Once you have studied at least two lessons from the link (and memorized the formula for the Rule), please attempt this exercise. If you get stuck, you can then reply with a clear listing of your efforts so far. Thank you!

 

[meano]

I will guess that the above is meant to say the following:

. . . . .\(\displaystyle y\, =\, \sqrt{x\,}\, =\, x^{\frac{1}{2}}\)

. . . . .\(\displaystyle y'\, =\, \left(\dfrac{1}{2}\right)\,x^{\frac{1}{2}-1}\)

Yes that is what I meant, wasn't sure how to write it how you did.

I will guess that you are familiar with how to differentiate 2x + 4. Since you don't mention or demonstrate the Quotient Rule, I will guess that you haven't covered that (though I have no idea how you're expected to do this without that Rule). Since we cannot teach courses here, please try online resources, such as are listed here.

I will have a look at this link. Thanks