F(x)=(x+3)^2 find c so that f’(c)=0?

1 Answer
Feb 21, 2018

I would say no value for #c#.

Explanation:

If #F(x)# is the antiderivative of #f(x)# in this case, then we have

#F(x)=(x+3)^2#

#f(x)=F'(x)#

#=2(x+3)*1# (by the chain rule)

#=2(x+3)#

Expanding, we get

#f(x)=2x+6#

Now, the question asks for #f'(c)=0#, so we first need to convert to #f(c)#.

#:.f(c)=2c+6#

#f'(c)=2#

So, there is no value for #c# that makes the equation equal to #0#.