Question

F(x) = (3x ^ 2 + 6x + 3)/(sqrt(x)) then :

Answer 1

Given: A function's derivative is given:

`f^(\prime)(x)=\frac{3(3x-1)(x+1)}{2x^{(3)/(2)}}`

Required: To determine the value of f'(3).

Explanation: The value of f'(3) can be determined by substituting x=3 in f'(x) as follows-

`f^(\prime)(3)=\frac{3[(3*3)-1](3+1)}{2*3^{(3)/(2)}}`

Further solving,

`\begin{gathered} f^(\prime)(3)=\frac{3*8*4}{2*3^{(3)/(2)}} \\ =\frac{16}{3^{(1)/(2)}} \end{gathered}`

On further solving the equation, we get

`\begin{gathered} f^(\prime)(3)=(16)/(1.7321) \\ =9.2376 \end{gathered}`

Final Answer:

`f^(\prime)(3)=9.2376`