Apakah extrema f (x) = e ^ x (x ^ 2 + 2x + 1)?

Jawapan:

x = -3 atau x = -1

Penjelasan:

# f = e ^ x, g = x ^ 2 + 2x + 1 #

# f '= e ^ x, g' = 2x + 2 #

#f '(x) = fg' + gf '= e ^ x (2x + 2) + e ^ x (x ^ 2 + 2x + 1) = 0 #

# e ^ x (2x + 2 + x ^ 2 + 2x + 1) = 0 #

# e ^ x (x ^ 2 + 4x + 3) = 0 #

# e ^ x (x + 3) (x + 1) = 0 #

# e ^ x = 0 atau x + 3 = 0 atau x + 1 = 0 #

tidak mungkin, # x = -3 atau x = -1 #

#f (-3) = e ^ -3 (9-6 + 1) = 0.199 #-> maks

#f (-1) = e ^ -1 (1-2 + 1) = 0 #-> min