Question

If f(x) = 2x5/3, what is the instantaneous rate of change of f(x) at x = 8?

StartFraction 16 Over 3 EndFraction
StartFraction 32 Over 3 EndFraction
StartFraction 40 Over 3 EndFraction
StartFraction 44 Over 3 EndFraction

Answer 1

f(x) = 2x^(5/3)

f'(x) = (10/3)x^(2/3)

f'(8) = (10/3)(8^(2/3)) = (10/3)(4) = 40/3