Project 7
Note: Use Matlab powers to do the following problems the easy way.
 Find all the minimums and maximums of the following functions.
𝒚 = 𝒙𝟒 − 𝟓𝒙𝟐 − 𝒙 + 𝟏
−𝟐<𝒙<𝟐
−𝒙𝟐
𝒚=𝒆
−∞<𝒙<∞
𝟑𝒆−𝒙 + 𝟓𝒆𝟑𝒙
𝒚=
𝟏<𝒙<𝟓
𝟕𝒙𝟐
 The distance between the Earth and the Mercury may be defined as
𝒅 = √(𝑿𝒆 − 𝑿𝒎 )𝟐 + (𝒀𝒆 − 𝒀𝒎 )𝟐 ,
where
𝟐𝝅𝒕)
𝑿𝒎 = −𝟏𝟏. 𝟗𝟎𝟖𝟒 + 𝟓𝟕. 𝟗𝟏𝟏𝟕𝐜𝐨𝐬 (
)
𝟖𝟕. 𝟗𝟕
𝟐𝝅𝒕)
𝒀𝒎 = 𝟓𝟔. 𝟔𝟕𝟒𝟏𝒔𝒊𝒏 (
)
𝟖𝟕. 𝟗𝟕
𝟐𝝅𝒕)
𝑿𝒆 = −𝟐. 𝟒𝟗𝟖𝟕 + 𝟏𝟒𝟗. 𝟔𝟎𝟒𝟏𝐜𝐨𝐬 (
)
𝟑𝟔𝟓. 𝟐𝟓
𝟐𝝅𝒕)
𝒀𝒆 = 𝟏𝟒𝟗. 𝟓𝟖𝟑𝟐𝒔𝒊𝒏 (
)
𝟑𝟔𝟓. 𝟐𝟓
Find the minimum and the maximum distance between the Earth and the Mercury over the first
1000 days. What days do these maximum and minimum occur? In the above equations, t and d
represent the number of days and distance in gigameters (109 𝑚𝑒𝑡𝑒𝑟𝑠), resprrectivley.