Let f(x)=3x^(1/3)(x^3-7). evaluate the specific values of: a: f prime(1)= b: f prime(4)= ?

1 Answer
SCooke
Jun 27, 2018

#f’(1) = -4#
#f’(4) = 0.222#

Explanation:

First simplify the expression and obtain the first derivative.
#3x^(1/3)(x^3-7) = 3x – 21x^(1/3)#
#f’(x) = 3 – 7x^(-2/3)#
NOW we can evaluate this expression at #x = 1 and x = 4#

#f’(1) = 3 – 7(1)^(-2/3)# ; #f’(1) = 3 - 7 = -4#
#f’(4) = 3 – 7(4)^(-2/3)# ; #f’(4) = 3 - 2.78 = 0.222#

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