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The function is $\"f(x)=x^3\"$ .

First evaluate $\"f(a)\"$ .

Substitute $\"x=a\"$ in $\"f(x)\"$ .

$\"f(a)=a^3\"$ .

Now evaluate $\"f(a+h)\"$ .

Substitute $\"x=a+h\"$ in $\"f(x)\"$ .

$\"f(a+h)=(a+h)^3\"$

$\"f(a+h)=a^3+3a^2h+3ah^2+h^3\"$ .

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Find $\"\\frac{f(a+h)-f(a)}{h}\"$ .

Substitute $\"f(a)=a^3\"$ and $\"f(a+h)=a^3+3a^2h+3ah^2+h^3\"$ in the above function.

$\"\\frac{f(a+h)-f(a)}{h}=\\frac{a^3+3a^2h+3ah^2+h^3-a^3}{h}\"$

$\"=\\frac{h^3+3a^2h+3ah^2}{h}\"$

$\"=\\frac{h(h^2+3a^2+3ah)}{h}\"$

$\"\\frac{f(a+h)-f(a)}{h}=h^2+3ah+3a^2\"$ .

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$\"\\frac{f(a+h)-f(a)}{h}=h^2+3ah+3a^2\"$ .