Question

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

Answer 1

`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`