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Find the difference quotientwhere h= 0, for the function below.hf(x) = 3x²-8Simplify your answer as much as possible.f(x + n) - f(x)0믐hХ2

Find The Difference Quotientwhere H 0 For The Function Belowhfx 3x8Simplify Your Answer As Much As Possiblefx N Fx0믐hХ2 class=

Sagot :

Given the function:

[tex]f(x)=3x^2-8[/tex][tex]\begin{gathered} f(x+h)=3(x+h)^2-8 \\ f(x+h)=3(x^2+2xh+h^2)-8 \end{gathered}[/tex]

Thus,

[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h} \\ \Rightarrow\frac{3(x^2+2xh+h^2)-8-(3x^2-8)}{h} \end{gathered}[/tex][tex]\frac{3x^2+6xh+3h^2-8-3x^2+8}{h}[/tex][tex]\frac{6xh+3h^2}{h}[/tex]

Hence, the final answer is:

[tex]\begin{gathered} \frac{3h(2x+h)}{h} \\ \Rightarrow3(2x+h) \\ \end{gathered}[/tex]

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