Find the absolute maximum value for the function f(x) = x^2 − 4, on the interval [–3, 0) U (0, 2].

Mathematics

1 answer:

Andreyy892 years ago

5 0

Answer:

Step-by-step explanation:

The function $y=x^2 -4$ is

decreasing for all $x\in [-3,0);$
is increasing for all $x\in (0,2]$

(see attached diagram for details).

The maximum value of the function is at endpoints -3 or 2. find y(-3) and y(2):

$y(-3)=(-3)^2-4=9-4=5\\ \\y(2)=4^2-4=0$

So, the maximum value is 5.

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A delivery truck is transporting boxes of two size: the combined weight of a large box and a small box is 65 pounds. The truck i

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pretty much about the same as before.

a = weight of a large box

b = weight of a small box.

we know their combined weight is 65 lbs, thus a + b = 65.

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$\bf \begin{cases} a+b=65\\ \boxed{b}=65-a\\ \cline{1-1} 60a+55b=3775 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{60a+55\left( \boxed{65-a} \right)=3775} \\\\\\ 60a+3575-55a=3775\implies 5a+3575=3775\implies 5a=200 \\\\\\ a=\cfrac{200}{5}\implies \blacktriangleright a = 40 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=65-a\implies }b=65-40\implies \blacktriangleright b=25\blacktriangleleft$