Three less than four times m is 100. Find m

Mathematics

1 answer:

Sergio [31]4 years ago

5 0

4m - 3 = 100
4m = 103
m = 25 3/4

Hope this helps!

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Given f '(x) = (2 - x)(6 - x), determine the intervals on which f(x) is increasing or decreasing. (2 points)

weeeeeb [17]

Answer:

Decreasing (2, 6); increasing on (-∞, 2) U (6, ∞)

Step-by-step explanation:

To determine where $f(x)$ is increasing or decreasing, we set $f'(x)=0$ and check for the intervals.

We see that $f'(x)=0$ when either $x=2$ or $x=6$ . Therefore, we'll need to check the intervals $(-\infty,2)$ , $(2,6)$ , and $(6,\infty)$

For the interval $(\infty,2)$ , we can pick $x=0$ . This means that $f'(0)=(2-0)(6-0)=(2)(6)=12>0$ , showing that $f(x)$ increases on the interval $(-\infty,2)$

For the interval $(2,6)$ , we can pick $x=4$ . This means that $f'(4)=(2-4)(6-4)=(-2)(2)=-4$ , showing that $f(x)$ decreases on the interval $(2,6)$

For the interval $(6,\infty)$ , we can pick $x=7$ . This means that $f'(7)=(2-7)(6-7)=(-5)(-1)=5>0$ , showing that $f(x)$ increases on the interval $(6,\infty)$