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  • 15-01-2019
  • Mathematics
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What’s the difference quotient simplified

Whats the difference quotient simplified class=

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gmany
gmany gmany
  • 21-01-2019

[tex]\text{Use}\ (a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\f(x+h)\to\text{exchange x to x + h}\\\\f(x)=x^3+3x\\\\f(x+h)=(x+h)^3+3(x+h)\\\\f(x+h)=x^3+3x^2h+3xh^2+h^3+3x+3h\\\\\dfrac{f(x+h)-f(x)}{h}=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-(x^3-3x)}{h}\\\\=\dfrac{x^3+3x^2h+3xh^2+h^3+3x+3h-x^3-3x}{h}\\\\=\dfrac{(x^3-x^3)+3x^2h+3xh^2+h^3+(3x-3x)+3h}{h}\\\\=\dfrac{3x^2h+3xh^2+h^3+3h}{h}\\\\=\dfrac{h(3x^2+3xh+h^2+3)}{h}\\\\=\boxed{3x^2+3xh+h^2+3}[/tex]

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