Opiskelupolut
Opiskelupolut
Opiskelupolut
Juuri 6 Derivaatta
Opiskelijapolut
Suositeltavia tehtäviä, saa ja voi laskea tietenkin muitakin tehtäviä.
1.1 Rationaalifunktio (1 h)
|
TASO 1 (AS 5-6) |
101 102 103 104 105 |
|
TASO 2 (AS 7-8) |
101 102 103 104 105 106 107 108 109 110 112 113 115 116 |
|
TASO 3 (AS 9-10) |
101 102 103 104 105 106 107 108 109 110 112 113 115 116 118 120 |
1.2 Rationaaliyhtälö- ja -epäyhtälö (2 h)
|
TASO 1 (AS 5-6) |
122 123 124 125 126 127 128 |
|
TASO 2 (AS 7-8) |
122 123 124 125 126 127 128 129 132 133 134 136 137 138 139 141 |
|
TASO 3 (AS 9-10) |
122 123 124 125 126 127 128 129 132 133 134 136 137 138 139 141 143 144 |
2.1 Funktion raja-arvo (1 h)
|
TASO 1 (AS 5-6) |
201 202 203 204 205 208 209 |
|
TASO 2 (AS 7-8) |
201 202 203 204 205 206 207 208 209 210 211 212 213 215 216 |
|
TASO 3 (AS 9-10) |
201 202 203 204 205 206 207 208 209 210 211 212 213 215 216 218 219 220 222 |
2.2 Toispuoleiset raja-arvot (1 h)
|
TASO 1 (AS 5-6) |
224 225 226 227 228 229 |
|
TASO 2 (AS 7-8) |
224 225 226 227 228 229 230 231 232 234 235 236 238 239 |
|
TASO 3 (AS 9-10) |
224 225 226 227 228 229 230 231 232 234 235 236 238 239 242 243 245 |
2.3 Funktion jatkuvuus (1 h)
|
TASO 1 (AS 5-6) |
246 247 248 249 250 251 |
|
TASO 2 (AS 7-8) |
246 247 248 249 250 251 252 253 254 255 257 259 |
|
TASO 3 (AS 9-10) |
246 247 248 249 250 251 252 253 254 255 257 259 260 262 264 265 |
3.1 Funktion muutosnopeus (1 h)
|
TASO 1 (AS 5-6) |
301 302 303 304 |
|
TASO 2 (AS 7-8) |
301 302 303 304 305 306 307 308 310 311 |
|
TASO 3 (AS 9-10) |
301 302 303 304 305 306 307 308 310 311 312 313 316 |
3.2 Derivaatan määritelmä (2 h)
|
TASO 1 (AS 5-6) |
317 318 319 320 321 |
|
TASO 2 (AS 7-8) |
317 318 319 320 321 322 323 324 325 326 328 329 |
|
TASO 3 (AS 9-10) |
317 318 319 320 321 322 323 324 325 326 328 329 330 331 333 |
3.3 Derivaattafunktio (2 h)
|
TASO 1 (AS 5-6) |
335 336 337 338 339 340 341 |
|
TASO 2 (AS 7-8) |
335 336 337 338 339 340 341 342 343 344 345 347 349 350 353 |
|
TASO 3 (AS 9-10) |
335 336 337 338 339 340 341 342 343 344 345 347 348 349 350 353 355 356 359 |
4.1 Polynomifunktion kulun tutkiminen (1 h)
|
TASO 1 (AS 5-6) |
401 402 403 404 405 |
|
TASO 2 (AS 7-8) |
401 402 403 404 405 406 408 410 411 412 414 |
|
TASO 3 (AS 9-10) |
401 402 403 404 405 406 408 410 411 412 414 416 417 419 |
4.2 Polynomifunktion ääriarvot (2 h)
|
TASO 1 (AS 5-6 ) |
421 422 423 424 425 426 427 |
|
TASO 2 (AS 7-8) |
421 422 423 424 425 426 427 428 429 430 431 432 434 438 441 |
|
TASO 3 (AS 9-10) |
421 422 423 424 425 426 427 428 429 430 431 432 434 435 436 438 439 441 442 443 445 448 449 |
5.1 Rationaalifunktion derivointi (1 h)
|
TASO 1 (AS 5-6) |
501 502 503 504 505 |
|
TASO 2 (AS 7-8) |
501 502 503 504 505 506 508 509 510 511 512 513 514 |
|
TASO 3 (AS 9-10) |
501 502 503 504 505 507 508 510 511 512 513 515 516 517 519 520 522 |
5.2 Rationaalifunktion ääriarvot (1 h)
|
TASO 1 (AS 5-6) |
523 524 525 526 527 528 |
|
TASO 2 (AS 7-8) |
523 524 525 526 527 528 529 530 531 532 534 535 536 539 |
|
TASO 3 (AS 9-10) |
523 524 525 526 527 528 529 530 531 532 534 535 536 539 541 543 544 546 |