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(t)=A_1t+A_0

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

(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(t)=\frac{1}{2}t+5

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

F(t)=\frac{1}{2}t

F(t)=\frac{1}{2}t+6

(d)1 mark

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

Exact value