Question

an unknown positive number is multiplied to itself, then multiplied by 4, then added to the square of another unknown positive number . this is then divided by the product of 5 and two unknown numbers to receive the value of z.
calculate the smallest possible value of z.

Answer 1

Answer:

I didn't exactly know what to do with the level of this problem, so I solved it with Differential Calculus. Pardon please... If it doesn't fit you.

Step-by-step explanation:

Take a look at the first attachment.

This can be written in the form of y = f(x).

• But I will not write it as y = f(x), because it may be confusing with the actual x and y.

So, let me differentiate once,

It gives that...

Z ' =

$\frac{4}{5} - \frac{1}{5 {a}^{2} }$

By the Principle of finding the local maxima of local minima, I will equate it equal to zero.

a = ( + or -) 1/2

Now, differentiating it once more ( Because I'm comfortable with the second derivative test),

Z " =

$\frac{2}{5 {a}^{3} }$

Now I'll put those values of a in this second derivative,

Z" =

$for \: a \: = \: \frac{ - 1}{2} \\ \frac{2}{5 {a}^{3} } = \: \frac{2}{ \frac{5}{ { (- 2)}^{3} } } \\ = \: \frac{ - 16}{5}$

Since for a = 1/2, Z" < 0,

a ( for - 1/2), is the minima.

So, the smallest possible vale of z will be - 16/5.

Here is a note for you, my friend...

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