Question:
Find the maximum and minimum values of:
![](https://static.wixstatic.com/media/20c892_1c6e976ddf534f8e8635eba632595c04~mv2.png/v1/fill/w_81,h_4,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_1c6e976ddf534f8e8635eba632595c04~mv2.png)
Answer:
a) Firstly differentiate the equation and set equal to zero to find values of x.
![](https://static.wixstatic.com/media/20c892_cc64a388a63e4f24ae714949b2258c17~mv2.png/v1/fill/w_79,h_36,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_cc64a388a63e4f24ae714949b2258c17~mv2.png)
Though not required in this example, to determine if the value for x is a minimum or maximum value you can perform double differentiation. Sub your x value into the equation, if the result is a positive number then this represents the minimum value, a negative result will suggest a maximum value.
![](https://static.wixstatic.com/media/20c892_34dd2f00d8164620a1a9f4843aba0b6a~mv2.png/v1/fill/w_80,h_26,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_34dd2f00d8164620a1a9f4843aba0b6a~mv2.png)
Now sub values for x into the original equation to find corresponding y values:
![](https://static.wixstatic.com/media/20c892_874cc6d11136467fb5ea98c869b55fd1~mv2.png/v1/fill/w_79,h_27,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_874cc6d11136467fb5ea98c869b55fd1~mv2.png)
b)
![](https://static.wixstatic.com/media/20c892_deae7338919442158a64608d9773d65c~mv2.png/v1/fill/w_79,h_36,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_deae7338919442158a64608d9773d65c~mv2.png)
Now sub in values of x into original equation to find corresponding values of y:
![](https://static.wixstatic.com/media/20c892_6b47a03655e748d0899237193ea0dd66~mv2.png/v1/fill/w_81,h_26,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_6b47a03655e748d0899237193ea0dd66~mv2.png)