AM-2067

Integrating standard functions

A Math · Secondary 4 · Hard · Integrating standard functions

The function has derivative

f'(x)=3(x+2)^2(x-1)

. The graph of

y=f(x)

passes through the point

(1,4)

. What is

f(x)

?

$f(x)=\tfrac{3}{4}x^4+2x^3-6x^2+4$
$f(x)=\tfrac{3}{4}x^4+3x^3-6x^2+4$
$f(x)=\tfrac{3}{4}x^4+3x^3-12x+\tfrac{49}{4}$
$f(x)=\tfrac{3}{4}x^4+2x^3-3x^2+4$

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