Apa persamaan garis tangen ke f (x) = (x-2) / (x ^ 2-4) pada x = -1?

Apa persamaan garis tangen ke f (x) = (x-2) / (x ^ 2-4) pada x = -1?
Anonim

Menjawab:

# y = -x #

Penjelasan:

#f (x) = (x-2) / ((x-2) (x + 2)) # (# a ^ 2-b ^ 2 = (a + b) (a-b) #)

#f (x) = 1 / (x + 2) = (x + 2) ^ - 1 #

#f '(x) = - (x + 2) ^ - 2 #

#f '(- 1) = - (- 1 + 2) ^ - 2 = - (1) ^ - 2 = -1 #

#f (-1) = (- 1 + 2) ^ - 1 = 1 ^ -1 = 1 #

# y-y_0 = m (x-x_0) #

# y-1 = -1 (x + 1) #

# y-1 = -x-1 #

# y = -x #