Use a graphing utility to approximate (to two decimal places) any relative

Mathematics

1 answer:

iogann1982 [59]3 years ago

3 0

Answer:

Relative minima at $(-\frac{7}{2} , -\frac{49}{4} )$ , and relative maxima DNE.

Step-by-step explanation:

The given function is f(x) = x (x + 7) ...... (1)

We have to calculate the relative maxima and relative minima at point (x, y).

Rearranging the function given above we get.

$y= x^{2} +7x = (x + \frac{7}{2} )^{2} -\frac{49}{4}$

⇒ $y+ \frac{49}{4} = (x + \frac{7}{2} )^{2}$

Now, this is an equation of parabola having vertex at $(-\frac{7}{2} , -\frac{49}{4} )$ and the axis is parallel to positive Y-axis.

Therefore, the function(1) has a relative minima at $(-\frac{7}{2} , -\frac{49}{4} )$ , and the relative maxima DNE. (Answer)

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PLEASE HELP!!!

pogonyaev

Step-by-step explanation:

Part A:

Let $m$ be the number of mittens and $s$ be the number of scarves. Then we have the inequalities:

$s+m\leq 30.$ This says Nivyana and Ana cannot make more than 30 scarves

$50s+25m\geq 1000.$ This says that Nivyana and Ana have to earn at least $1000.

Part B:

The graph is attached.

Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.

The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.

Part C:

From the graph we get two possible solutions:

15 scarves & 10 mittens

25 scarves & 5 mittens.

These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)