Opiskelupolut
Opiskelupolut 2024
Opiskelupolut
Juuri 6 Derivaatta
Opiskelijapolut
Suositeltavia tehtäviä, saa ja voi laskea tietenkin muitakin tehtäviä.
1.1 Funktion kertausta (1 h)
|
TASO 1 (AS 5-6) |
101 102 103 104 105 106 107 111 |
|
TASO 2 (AS 7-8) |
101 102 103 104 105 106 107 108 109 110 111 113 115 116 119 |
|
TASO 3 (AS 9-10) |
101 102 103 104 105 106 107 108 109 110 111 113 115 116 119 120 121 |
1.2 Raja-arvo (1 h)
|
TASO 1 (AS 5-6) |
123 124 125 126 127 128 129 |
|
TASO 2 (AS 7-8) |
123 124 125 126 127 128 129 130 131 132 133 135 136 137 139 141 |
|
TASO 3 (AS 9-10) |
123 124 125 126 127 128 129 130 131 132 133 135 136 137 139 141 143 144 |
1.3 Funktion jatkuvuus (1 h)
|
TASO 1 (AS 5-6) |
146 147 148 149 150 151 153 154 |
|
TASO 2 (AS 7-8) |
146 147 148 149 150 151 152 153 154 155 156 157 160 162 |
|
TASO 3 (AS 9-10) |
146 147 148 149 150 151 152 153 154 155 156 157 160 162 163 164 |
2.1 Funktion muutosnopeus (1 h)
|
TASO 1 (AS 5-6) |
201 202 203 204 205 206 207 218 |
|
TASO 2 (AS 7-8) |
201 202 203 204 205 206 207 208 209 210 211 213 214 216 218 |
|
TASO 3 (AS 9-10) |
201 202 203 204 205 206 207 209 210 211 213 214 215 216 218 220 |
2.2 Derivaatan määritelmä (1 h)
|
TASO 1 (AS 5-6) |
221 222 223 224 225 226 |
|
TASO 2 (AS 7-8) |
221 222 223 224 225 226 227 228 229 231 233 234 235 237 |
|
TASO 3 (AS 9-10) |
221 222 223 224 225 226 227 228 229 231 233 234 235 237 238 240 |
2.3 Derivaattafunktio (2 h)
|
TASO 1 (AS 5-6) |
241 242 243 244 245 246 247 248 249 250 |
|
TASO 2 (AS 7-8) |
241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 261 263 264 265 |
|
TASO 3 (AS 9-10) |
241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 261 263 264 265 266 267 268 |
3.1 Polynomifunktion kasvaminen ja väheneminen (1 h)
|
TASO 1 (AS 5-6) |
301 302 303 304 305 306 307 |
|
TASO 2 (AS 7-8) |
301 302 303 304 305 306 307 308 309 310 311 312 313 314 316 317 |
|
TASO 3 (AS 9-10) |
301 302 303 304 305 306 307 308 309 310 311 312 313 314 316 317 320 |
3.2 Funktion ääriarvot (1 h)
|
TASO 1 (AS 5-6 ) |
322 323 324 325 326 327 328 |
|
TASO 2 (AS 7-8) |
322 323 324 325 326 327 328 329 330 331 332 333 334 336 338 |
|
TASO 3 (AS 9-10) |
322 323 324 325 326 327 328 329 330 331 332 333 334 336 338 339 340 |
4.1 Potenssifunktion derivaatta (1 h)
|
TASO 1 (AS 5-6) |
401 402 403 404 405 406 407 |
|
TASO 2 (AS 7-8) |
401 402 403 404 405 406 407 408 409 410 411 412 414 416 |
|
TASO 3 (AS 9-10) |
401 402 403 404 405 406407 408 409 410 411 412 414 416 417 419 |
4.2 Tulon ja osamäärän derivaatat (1 h)
|
TASO 1 (AS 5-6 ) |
422 423 424 425 426 427 |
|
TASO 2 (AS 7-8) |
422 423 424 425 426 427 428 429 430 431 432 434 437 438 |
|
TASO 3 (AS 9-10) |
422 423 424 425 426 427 428 429 430 431 432 434 437 438 439 442 443 |
4.3 Rationaalifunktion kulku ja ääriarvot (1 h)
|
TASO 1 (AS 5-6) |
444 445 446 447 448 449 450 |
|
TASO 2 (AS 7-8) |
444 445 446 447 448 449 450 451 452 453 455 457 458 |
|
TASO 3 (AS 9-10) |
444 445 446 447 448 449 450 451 452 453 455 457 458 460 461 |
4.4 Funktion potenssin derivaatta (2 h)
|
TASO 1 (AS 5-6 ) |
463 465 466 467 470 464 468 469 |
|
TASO 2 (AS 7-8) |
463 465 466 467 470 464 468 469 471 476 477 478 474 479 480 481 483 |
|
TASO 3 (AS 9-10) |
463 465 466 467 470 464 468 469 471 476 477 478 474 479 480 481 483 485 486 |
5.1 Eksponentti- ja logaritmifunktioita. Ketjusääntö (1 h)
|
TASO 1 (AS 5-6) |
501 502 503 504 50550 506 507 |
|
TASO 2 (AS 7-8) |
501 502 503 504 50550 506 507 508 509 510 511 512 513 514 515 516 |
|
TASO 3 (AS 9-10) |
501 502 503 504 50550 506 507 508 509 510 511 512 513 514 515 516 517 519 520 |
5.2 Yhdistetty funktio ja ketjusääntö (2 h)
|
TASO 1 (AS 5-6) |
522 523 524 525 526 527 528 529 530 531 |
|
TASO 2 (AS 7-8) |
522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 540 542 543 544 |
|
TASO 3 (AS 9-10) |
522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 540 542 543 544 546 547 549 550 553 |
6.1 Funktion suurin ja pienin arvo suljetulla välillä (1 h)
|
TASO 1 (AS 5-6) |
601 602 603 604 605 606 607 |
|
TASO 2 (AS 7-8) |
601 602 603 604 605 606 607 608 611 610 612 609 613 614 616 |
|
TASO 3 (AS 9-10) |
601 602 603 604 605 606 607 608 611 610 612 609 613 614 616 618 620 622 |
6.2 Sinin ja kosinin derivaatat (2 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 54 |
7.1 Tangentin käyttöä (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 |
7.2 Ääriarvosovelluksia (2 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 54 |