First you use the critical points that you found and plug the values into the second derivative test and you will find the local max and min.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUVrwQ_6pa2czyj_fo6DZBPnRq-R1-V_Oc89s9VCLCsRfobpwVbX2ywARquJlzxSuIph4zAHwsMWi14HMtFNGxli80L-gfRNpHrFOTl1RKTKWuJBIlqKy-xcwOQ_39CcpK9gZtKyL_NXs/s400/slide+1.bmp)
Next you find all possible inflection points by making the second derivative equal to zero and solve for x.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidcMTcJwR40fKtWXiE5AnIpvg2IrAEBVKGFkZf_B-59r1h_nt3Hjh3lLQpBKglvkDKasyhRY4qKy1zbXSnOvBfPA-sGFqCt2PnN0O8H4HPUP0UWZixxd3q9sMNaQu98yNUf7D_f9rnQgU/s400/slide+2.bmp)
After Figuring all that stuff out you solve for the original function and use the critical points that we have found for the x values.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgARTdUdCBU9IV2_Mbvz-MfE8az0YVosoWfD1LN0nVm8OnW9c3M3Kpar8RP41n_VwtrUND3dmQM3ORXa7SAJMmxTy8L-NC2ZaqnpKN0rP20b90SJJqHo9TbfQsW3o-6U60GRwfDuhRh8CY/s400/slide+3.bmp)
Now you need to find out if it is concave up or concave down.
To find the that out you need to choose a value from the ranges and plug it in to the second derivative formula which is f ''(x) = 4 - 12x
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidvc28QP83Gy0V2joOMiV5_8NDl23Vsx2SuV387FFMr3Fkev7SmyLmFEdd-ExkRROVLlwbFF_5XiPhUjhZ44Lou2qGVOefmhY8IlQgUZJ2VIPA_rAt2pGiQLDJFJdmlZZSeCreIAX4rI8/s400/slide+4.bmp)
Next you solve for f(x) but this time you use the infliction points that we found for the x value.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhd47Uh99V0AgvPXED1_UKV7u3H15picIqTnjxPoH0HPD31i_PvhwI3Gd7QPWAAsLo03a0jbowOJL3wP06441H1DRAQVIiG5hOOxQFmYiMKacH7YNC2NQjzQqGIwU4nIqEVO5d4VA88_K4/s400/slide+5.bmp)
This next picture is a picture of the second derivative i think. it shows when the graph is concave up and concave down.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwsXOQ4hNvv_hGRpPWvzDlpD9SVE1CcTP6WGR25yAfvPcfSZ-Yfw2ZD12ATQ5tCsRU6Cf9W60ES_5mZp309ENwDCw4vTAxg5n-HjPHGNlUghO5REnODDskTnhmT0L7M3B6YzI7jvdMQbE/s400/slide+6.bmp)
Well thats all for today tune in next time. Next scribe post will be featuring Shelly.
Rguy out.
No comments:
Post a Comment