Question

Can someone tell me if these answers for question 1 are correct and also help with the last 3? The lab is attached

Answer 1

i would have gone with your first answer for the domain
the arrow suggests that it goes to the left without end, making the domain \((-\infty, 6]\)

Answer 2

b) is correct, \(f(0)\) is positive because \(f(0)=2\)

Answer 3

local min and local max points are exactly what they sound like. look at the graph and find the spots that are highest and lowest (where slope changes from positive to negative, or vice versa)

Answer 4

interesting that there are in fact two "b"s

Answer 5

for the local max (-1,4) and (2,4)?

Answer 6

looks good @oroutdoors

Answer 7

how about my answers for part c?

Answer 8

correct

Answer 9

Thanks

Answer 10

part d you need the local min as well (1,0)

Answer 11

for the intervals, just find where slop is increasing or decreasing. you use your local mins and maxes as boundary points. e.g., slop is increasing from \[(-infinity,-1]\]

Answer 12

slope

Answer 13

when you find function intervals where f(x) is > 0 just be sure not to include the exact value of x where f(x) = 0. Use ( and not [ and ) and not ]

Answer 14

good luck, i gotta run

Answer 15

Okay thanks for your help!

Answer 16

actually at x = -1 slope is zero since it's at that point changing from positive to negative, so you may want to use ) instead of ]

Answer 17

idk if your teacher will pay attention to that

Answer 18

yw night!

Answer 19

night!

Answer 20

e) Increasing (-Infinity, -1] and [1,2] decreasing [-1,1] and [2,6]

Answer 21

all your numbers look correct

I'm a little concerned about the brackets around your intervals though. Just because at -1 the function is not increasing or decreasing, it is 0. This will be evident when you take calculus 1 and find the 1st derivative of your function at that point is zero, i.e., slope of your tangent line is zero. I would write the interval as (-infinity, -1) and not ] just because this point isn't in the positive interval. IDK what your teacher will say, or if he/she will care.... You could ask and get some brownie points.

Answer 22

really, the function is only increasing up to 0.999999999999999999.....forever.... until x=1, then the function is neither increasing or decreasing. Similarly, visually moving toward the right of the graph from that point x=1, it is decreasing starting at x=1.00000000000000...........000000001 with infinite zeros.

Answer 23

Thanks you're awesome. would [2,4] be correct for f? I'm not so sure on that one