Determine a polynomial from its derivative and a boundary condition practice questions | Mathematical Methods (Year 12, VCE Units 3 & 4, Antiderivatives, Antiderivative families and applications)

(a)3 marks

Use F = P + C, where P has zero constant term. Enter 0 for the constant coefficient of P

Enter every coefficient in descending powers, including zero for an absent term

P(x)=A_2x^{2}+A_1x+A_0

\(\text{coefficient of }x^{2}\) \(\text{coefficient of }x\) \(\text{constant coefficient}\)

(b)1 mark

Find C in F = P + C

Exact value

(c)1 mark

Select the unique function satisfying both the gradient and boundary condition

F(x)=-\frac{3}{2}x^{2}-2x

F(x)=-\frac{3}{2}x^{2}-2x-1

F(x)=-\frac{3}{2}x^{2}-2x-2

F(x)=\frac{3}{2}x^{2}+2x-2

(d)1 mark

Find \(F(-\frac{3}{2})\)

Exact value