Thread: sign chart, finding intervals of increase, decrease?

(x+1)^5-5x-2
f'(x)=5(x+1)^4-5
x=-2,0
if i make a sign chart, i would have to do all 4 factors (x+1) which means all negative signs would then be made positive.
but in the answer section, it says between -2 and 0, the function is decreasing, which means in the sign chart, it should be negative....
i hope im making sense..
what am i overlooking here?

Hi

f'(x) = 5(x+1)^4-5 = 5x(x+2)[(x+1)²+1]

Since 5[(x+1)²+1] > 0 the sign of f' is the same as x(x+2), therefore negative between -2 and 0

hmm, can you explain how you factored out f'(x)=5(x+1)^4-5 to be 5x(x+2)[(x+1)^2+1]?

f'(x) = 5(x+1)^4-5 = 5[(x+1)^4 - 1]

(x+1)^4 - 1 = [(x+1)²]²-1 = [(x+1)²-1][(x+1)²+1] = (x+1-1)(x+1+1)[(x+1)²+1] = x(x+2)[(x+1)²+1]

It is a matter of using a²-b² = (a-b)(a+b)