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motikmotik
3 years ago
5

Find the intervals on which the function is increasing or decreasing.

Mathematics
1 answer:
Assoli18 [71]3 years ago
6 0
To solve this, you have to know that the first derivative of a function is its slope. When an interval is increasing, it has a positive slope. Thus, we are trying to solve for when the first derivative of a function is positive/negative.

f(x)=2x^3+6x^2-18x+2
f'(x)=6x^2+12x-18
f'(x)=6(x^2+2x-3)
f'(x)=6(x+3)(x-1)
So the zeroes of f'(x) are at x=1, x=-3
Because there is no multiplicity, when the function passes a zero, he y value is changing signs.
Since f'(0)=-18, intervals -3<x<1 is decreasing(because -3<0<1)
Thus, every other portion of the graph is increasing.
Therefore, you get:

Increasing: (negative infinite, -3), (1, infinite)
Decreasing:(-3,1)
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6 0
3 years ago
What is - 1/6 + (-7/4) this is 7th gradr math
DedPeter [7]

Hello Bubbleshi !

The first step you need to do is get everything in like terms.

- 1/6 and - 7 /4

Look at the denominator (number on the bottom)

6 and 4 go into 12, so lets check that out.

-1/6 , how can we get 12 from the denominator? Multiply it by 2.

So you multiply both the numerator (number on the top) and the denominator.

-1/6 becomes -2/12.

With -7/4, you want to get the 4 as a 12 (like terms!) so once again you multiply it by 3, and multiply the numerator as well.


-7/4 becomes -21/12.

-2/12 + (-21/12) is your final form of the problem.

You add -2 and -21 in the numerator, which is -23.

So its -23/12 which is your final answer.

Let me know if you need any more help!

8 0
4 years ago
Lane's arm span is 61 inches. If his height is 1⁄4 foot longer than his arm span, how tall is he? feet and inches
melamori03 [73]
If lane's are span is 61 inches. his height is 1/4 foot long than his arm span. his height is <span>5 ft 3 inches </span> 
6 0
3 years ago
A media poll of 500 air travelers surveyed in national airports found that 370 favor tighter security procedures in boarding pla
serg [7]

Answer:

92% Confidence interval:  (0.7078,0.7722)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 500

Number of travelers who favor tight security, x = 370

\hat{p} = \dfrac{x}{n} = \dfrac{370}{500} = 0.74

92% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.08} = \pm 1.645

Putting the values, we get:

0.74\pm 1.645(\sqrt{\dfrac{0.74(1-0.74)}{500}}) = 0.74\pm 0.0322\\\\=(0.7078,0.7722)

3 0
4 years ago
Solve the equation x2+6x+8=0?
Aleksandr-060686 [28]

Answer:

28 , 28, -14

Step-by-step explanation:

x2+6x+8=0

4(2)+6(2)+8=0

8+12+8=0

28=0

x2+6x+8=0

-4(2)+6(2)+8=0

8+12+8=0

28=0

x2+6x+8=0

-8(2)+6(-1)+8=0

-16-6+8

-14=0

3 0
4 years ago
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