Answer
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Work Step by Step
g'(x) = f'(x)(1)
All the values of g'(x) are equal to those of f'(x)
h'(x) = 2f'(x)(1)
h'(-2) = 2(f'(-2)) = 2(4) = 8
h'(-1) = 2(f'(-1)) = 2($\dfrac{2}{3}$) = $\dfrac{4}{3}$
h'(0) = 2(f'(0)) = 2(-$\dfrac{1}{3}$) = -$\dfrac{2}{3}$
h'(1) = 2(f'(1)) - 2(-1) - -2
h'(2) = 2(f'(2)) = 2(-2) = -4
h'(3) = 2(f'(3)) = 2(-4) = -8
r'(x) = f'(-3x)(-3) = -3(f'(-3x))
r'(-2) = -3(f'(-3(-2))) = -3(f'(6)) = Not possible since f'(6) has not been given.
r'(-1) = -3(f'(-3(-1))) = -3(f'(3)) = -3(-4) = 12
r'(0) = -3(f'(-3(0))) = -3(f'(0)) = -3(-$\dfrac{1}{3}$) = 1
r'(1) = -3(f'(-3(1))) = -3(f'(-3)) = Not possible since f'(-3) has not been given.
r'(2) = -3(f'(-3(2))) = -3(f'(-6)) = Not possible since f'(-6) has not been given.
r'(3) = -3(f'(-3(3))) = -3(f'(-9)) = Not possible since f'(-9) has not been given.
s'(x) = f'(x + 2)(1)
s'(-2) = f'((-2) + 2) = f'(0) = -$\dfrac{1}{3}$
s'(-1) = f'((-1) + 2) = f'(1) = -1
s'(0) = f'((0) + 2) = f'(2) = -2
s'(1) = f'((1) + 2) = f'(3) = -4
s'(2) = f'((2) + 2) = f'(4) = Not possible since f'(4) has not been given.
s'(3) = f'((3) + 2) = f'(5) = Not possible since f'(5) has not been given.
