Antiderivative with an initial condition

Practise antiderivative with an initial condition with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

A function satisfies $f\prime(x)=6x^2-4x$ and $f(1)=5$. (a) Find f(x). [3 marks] (b) Find $f(2)$. [1 marks]

Worked explanation

• Part (a)

  Integrate to obtain $f(x)=2x^3-2x^2+C$. Since $f(1)=5$, $C=5$.

• Part (b)

  $f(2)=2(8)-2(4)+5=13$.

(a) $f(x)=2x^3-2x^2+5$.; (b) $13$.

Original VectorPaths practice; not an official VCAA question or marking rubric.