Question

dado f(x)=x³+3x, hallar f(x+h)-f(x)​

Answer 1

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f(x)=x³+3x, hallar f(x+h)-f(x)

Reemplazando:

f(x+h)=(x+h)³+3(x+h)

f(x)=x³+3x

f(x+h)-f(x) = (x+h) ³+3(x+h) - (x³+3x)

f(x+h)-f(x) = (x+h) ³+ 3x + 3h - x³- 3x

f(x+h)-f(x) = (x+h) ³ + 3h - x³

f(x+h)-f(x) =(x³+3x²h+3xh²+h³)+ 3h-x³

f(x+h)-f(x) = 3x²h + 3xh² + h³ + 3h

f(x+h)-f(x) = 3xh( x + h) + h(h² + 3)

f(x+h)-f(x) = h[3x( x + h) + h² + 3]