Determine a polynomial from its derivative and a boundary condition practice questions | Mathematical Methods (Year 12, VCE Units 3 & 4, Integration, Average value, total change and kinematics)

(a)2 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(u)=A_1u+A_0

\(\text{coefficient of }u\) \(\text{constant coefficient}\)

(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(u)=-\frac{1}{2}u+6

F(u)=\frac{1}{2}u+5

F(u)=-\frac{1}{2}u

F(u)=-\frac{1}{2}u+5

(d)1 mark

Find \(F(\frac{1}{2})\)

Exact value