Sally is differentiating a function #f#. She has gotten the answer, #f'(x) = −x^-2#. Write 3 possibilities for the function which Sally differentiated?

1 Answer
Mar 23, 2017

I get only two possibilities
1. #f(x)=1/x+C_1#
2. #f(x)=1/x#

Explanation:

Although it appears from the text to be a question on differentiation. However, if you look closely it is actually a question of integration.

Given #f'(x)=-x^-2#, need to find out #f(x)# and state three possibilities.
Integrating both sides we get
#intf'(x)dx=int-x^-2 dx#
#=>f(x)=-int1/x^2 dx#

Using the basic form
#intx^n dx=1/(n+1)x^(n+1)#
we get

#f(x)=-(-1/x+C)#
where #C# is a constant of integration.
#=>f(x)=1/x+C_1#
where #C_1# is a constant of integration.
I get only two possibilities
1. #f(x)=1/x+C_1#
2. #f(x)=1/x#