Using quick and dirty analysis with a 10M Digital Elevation Model (DEM), I produced this dataset which shows the high and low points for each county. The highest point in Tennessee (as any native would know) is in Sevier County at Clingmans Dome, at 6644.33' The lowest point is in Davidson County at a Vulcan Materials quarry at just 90.18' above sea level. Of course, this doesn't include locations that are underground, so let's qualify that this is the lowest point that is not underground. Below is the table if you want to look at your home county.
| County | High Point Map | High Point
Elevation | Low Point Map | Low Point Elevation |
| Anderson | 36.198101,-84.230138 | 3527.87 | 36.021527,-84.324953 | 757.79 |
| Bedford | 35.659490,-86.304398 | 1355.83 | 35.578287,-86.637268 | 630.75 |
| Benton | 35.852453,-88.206064 | 683.96 | 36.018287,-88.003935 | 338.01 |
| Bledsoe | 35.743564,-84.991342 | 2680.95 | 35.434861,-85.335046 | 707.66 |
| Blount | 35.568564,-83.70625 | 5526.05 | 35.874212,-84.009953 | 803.36 |
| Bradley | 35.149027,-85.023935 | 1492.87 | 35.278101,-84.747638 | 674.45 |
| Campbell | 36.198009,-84.230324 | 3527.57 | 36.223564,-84.092916 | 831.69 |
| Cannon | 35.866064,-85.976157 | 2094.81 | 35.832546,-86.178472 | 592.91 |
| Carroll | 35.855509,-88.237731 | 710.89 | 36.062083,-88.691064 | 324.19 |
| Carter | 36.104768,-82.122361 | 6284.05 | 36.374490,-82.295509 | 1388.81 |
| Cheatham | 36.127268,-87.021990 | 910.62 | 36.368657,-87.250138 | 356.41 |
| Chester | 35.453287,-88.463287 | 742.61 | 35.464490,-88.683101 | 365.37 |
| Claiborne | 36.569120,-83.835231 | 3205.18 | 36.375787,-83.450694 | 1014.49 |
| Clay | 36.588472,-85.471898 | 1409.65 | 36.558009,-85.498472 | 484.78 |
| Cocke | 35.715046,-83.255509 | 6351.13 | 36.001064,-83.237268 | 994.73 |
| Coffee | 35.454120,-85.893842 | 2025.99 | 35.465046,-86.246620 | 787.82 |
| Crockett | 35.837638,-89.263842 | 484.07 | 35.992824,-89.190694 | 269.90 |
| Cumberland | 35.781157,-84.978472 | 3053.74 | 35.825509,-84.781805 | 869.10 |
| Davidson | 36.064675,-86.783842 | 1158.98 | 36.125601,-86.922546 | 90.18 |
| Decatur | 35.495601,-88.021157 | 707.76 | 35.663287,-88.025138 | 345.94 |
| DeKalb | 35.845509,-85.892083 | 1327.68 | 36.107453,-85.851805 | 473.00 |
| Dickson | 36.107546,-87.426435 | 963.81 | 36.328287,-87.231805 | 357.96 |
| Dyer | 36.141527,-89.381435 | 512.22 | 35.923472,-89.643842 | 229.51 |
| Fayette | 35.039027,-89.220972 | 671.75 | 35.31125,-89.632916 | 248.85 |
| Fentress | 36.155416,-85.084398 | 1871.47 | 36.453472,-85.088472 | 649.64 |
| Franklin | 35.219398,-85.887268 | 2033.18 | 34.98875,-85.899120 | 616.89 |
| Gibson | 35.808194,-88.755138 | 573.54 | 36.014953,-89.194305 | 269.88 |
| Giles | 35.456064,-87.129120 | 1169.98 | 34.997731,-87.030509 | 558.54 |
| Grainger | 36.375046,-83.346157 | 2518.80 | 36.089305,-83.659953 | 849.11 |
| Greene | 36.061342,-82.627453 | 4853.91 | 36.180509,-83.165879 | 1023.19 |
| Grundy | 35.320694,-85.563101 | 2383.62 | 35.525324,-85.681712 | 871.39 |
| Hamblen | 36.227453,-83.332638 | 1953.45 | 36.125046,-83.235509 | 998.11 |
| Hamilton | 35.003842,-85.345509 | 2152.00 | 35.064027,-85.189675 | 454.15 |
| Hancock | 36.423287,-83.196898 | 2628.93 | 36.413472,-83.385694 | 1077.27 |
| Hardeman | 35.139675,-89.138287 | 693.75 | 35.423194,-89.087361 | 309.65 |
| Hardin | 35.058194,-88.001157 | 844.66 | 35.244583,-88.168009 | 316.15 |
| Hawkins | 36.408101,-82.706990 | 3117.49 | 36.312824,-83.238564 | 1063.98 |
| Haywood | 35.398009,-89.185972 | 502.89 | 35.575509,-89.498009 | 254.51 |
| Henderson | 35.500601,-88.440601 | 704.97 | 35.624398,-88.247453 | 372.84 |
| Henry | 36.385787,-88.297453 | 652.84 | 36.298657,-88.144953 | 343.82 |
| Hickman | 35.931157,-87.303379 | 982.93 | 35.898563,-87.690970 | 372.19 |
| Houston | 36.190787,-87.579398 | 864.76 | 36.250509,-87.924583 | 355.39 |
| Humphreys | 36.137638,-87.552175 | 888.46 | 35.966342,-87.992731 | 347.96 |
| Jackson | 36.398009,-85.527175 | 1131.63 | 36.309490,-85.750138 | 496.76 |
| Jefferson | 35.901064,-83.298101 | 3632.70 | 36.058194,-83.694120 | 833.88 |
| Johnson | 36.338009,-81.706342 | 5503.51 | 36.340138,-81.999768 | 1955.74 |
| Knox | 36.111990,-83.766527 | 2090.51 | 35.944768,-83.914305 | 603.07 |
| Lake | 36.419212,-89.453009 | 325.80 | 36.444583,-89.383287 | 137.21 |
| Lauderdale | 35.833194,-89.479490 | 526.33 | 35.542546,-89.907453 | 208.89 |
| Lawrence | 35.434675,-87.223564 | 1101.81 | 35.008657,-87.574768 | 513.42 |
| Lewis | 35.490694,-87.276898 | 1074.79 | 35.618842,-87.447268 | 569.55 |
| Lincoln | 34.997824,-86.322361 | 1515.23 | 35.092268,-86.820787 | 597.60 |
| Loudon | 35.710416,-84.179305 | 1322.36 | 35.885046,-84.300324 | 736.14 |
| Macon | 36.429027,-85.897361 | 1101.22 | 36.439027,-86.110416 | 498.01 |
| Madison | 35.699305,-88.610231 | 663.67 | 35.688564,-89.069120 | 303.57 |
| Marion | 35.318564,-85.55875 | 2385.66 | 34.998287,-85.720046 | 589.58 |
| Marshall | 35.403657,-86.726157 | 1288.91 | 35.592824,-86.836712 | 582.62 |
| Maury | 35.459398,-87.129953 | 1175.66 | 35.715601,-87.255138 | 499.55 |
| McMinn | 35.273194,-84.509768 | 2344.62 | 35.471898,-84.635972 | 663.27 |
| McNairy | 35.288101,-88.534305 | 688.01 | 34.995416,-88.723194 | 357.17 |
| Meigs | 35.529490,-84.718657 | 1296.06 | 35.484490,-84.875046 | 680.49 |
| Monroe | 35.309212,-84.026620 | 5465.14 | 35.495324,-84.249490 | 807.00 |
| Montgomery | 36.33375,-87.432361 | 811.26 | 36.422453,-87.587731 | 342.32 |
| Moore | 35.342083,-86.530416 | 1266.39 | 35.143472,-86.369398 | 693.14 |
| Morgan | 36.107546,-84.415138 | 3339.63 | 35.975972,-84.570046 | 752.01 |
| Obion | 36.433842,-89.158472 | 552.90 | 36.251990,-89.433842 | 253.71 |
| Overton | 36.180694,-85.242175 | 2024.36 | 36.344212,-85.496435 | 580.12 |
| Perry | 35.488935,-87.726064 | 983.50 | 35.590509,-87.999583 | 355.28 |
| Pickett | 36.583101,-85.025046 | 1789.55 | 36.625138,-85.222083 | 635.91 |
| Polk | 35.000138,-84.529305 | 4221.98 | 35.225231,-84.628009 | 679.83 |
| Putnam | 36.100231,-85.243379 | 2058.95 | 36.142175,-85.804675 | 473.39 |
| Rhea | 35.543564,-85.102083 | 2040.89 | 35.538287,-84.898657 | 583.49 |
| Roane | 35.866527,-84.714212 | 2033.54 | 35.899212,-84.617175 | 674.52 |
| Robertson | 36.413287,-86.714305 | 928.57 | 36.554953,-87.132361 | 378.92 |
| Rutherford | 35.717916,-86.230138 | 1366.32 | 36.000138,-86.457731 | 463.74 |
| Scott | 36.163564,-84.441342 | 3260.67 | 36.598564,-84.605046 | 794.67 |
| Sequatchie | 35.372916,-85.319305 | 2393.83 | 35.270601,-85.433009 | 657.28 |
| Sevier | 35.562824,-83.498564 | 6644.33 | 35.944953,-83.686527 | 837.34 |
| Shelby | 34.998194,-89.909490 | 491.58 | 34.998657,-90.247731 | 186.33 |
| Smith | 36.140138,-86.063564 | 1249.70 | 36.249861,-85.926898 | 439.88 |
| Stewart | 36.344212,-87.781990 | 771.25 | 36.498935,-87.858564 | 333.41 |
| Sullivan | 36.437361,-82.129768 | 4298.70 | 36.545879,-82.611064 | 1150.04 |
| Sumner | 36.464768,-86.247916 | 1083.15 | 36.301064,-86.665879 | 402.06 |
| Tipton | 35.446527,-89.807453 | 457.22 | 35.400601,-90.147731 | 196.23 |
| Trousdale | 36.424675,-86.219305 | 1104.03 | 36.313287,-86.269953 | 436.87 |
| Unicoi | 35.989675,-82.490416 | 5503.71 | 36.154675,-82.441435 | 1572.52 |
| Union | 36.175879,-83.724675 | 2311.68 | 36.172731,-83.927083 | 912.70 |
| Van Buren | 35.577731,-85.433472 | 2144.16 | 35.818379,-85.430324 | 781.66 |
| Warren | 35.534768,-85.613101 | 1984.97 | 35.832175,-85.686805 | 644.28 |
| Washington | 36.217175,-82.370509 | 3548.47 | 36.440231,-82.438472 | 1259.83 |
| Wayne | 35.218379,-87.710416 | 1086.37 | 35.387175,-87.999768 | 357.30 |
| Weakley | 36.496527,-88.595046 | 601.77 | 36.217268,-88.953472 | 285.94 |
| White | 35.87875,-85.315231 | 2009.50 | 35.857361,-85.630046 | 642.88 |
| Williamson | 35.755509,-86.74125 | 1252.30 | 35.902916,-86.896342 | 369.54 |
| Wilson | 36.069861,-86.170787 | 1368.15 | 36.292546,-86.472083 | 438.46 |
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