Answered

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For the function f ( x ) = 3x² + 3x , evaluate and simplify. f ( x + h ) − f ( x )/ h

Sagot :

The function f is given by:

[tex]\begin{gathered} f(x)=3x^2+3x \\ f(x+h)=3(x+h)^2-3(x+h) \\ f(x+h)=3(x^2+2xh+h^2)-3(x+h) \\ f(x+h)=3x^2+6xh+3h^2-3x-3h \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{3x^2+6xh+3h^2+3x-3h-(3x^2+3x)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{6xh+3h^2+3h}{h}=6x+3+3h \end{gathered}[/tex]

Therefore, the correct answer is 6x + 3 + 3h

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