Given:
Find the critical numbers and open intervals on which the function is increasing or decreasing.
Would I simply compute the derivative of -x^3+1 and -x^2+2x seperately and solve each down?
Can anyone offer some instruction for piecewise functions ?
Thus:
y' =
and
and:
Critical point:
And the test intervals are:
Thus:
test value: -2
Sign of f'(x) on -2x+2 = -2
Sign of f'(x) on -3x^2 = -12
Conclusion: decreasing for x < 0 and decreasing for x > 0
and:
test value: 2
Sign of f'(x) on -2x+2 = -2
Sign of f'(x) on -3x^2 = -12
Conclusion: decreasing for x < 0 and decreasing for x > 0
is this correct or have i made a mistake ?