Infer primitive curves from a gradient function practice questions | Mathematical Methods (Year 12, VCE Units 3 & 4, Antiderivatives, Antiderivative families and applications)

(a)1 mark

Enter +1 for positive g (F increasing) or −1 for negative g (F decreasing), on each open interval. Infinity labels describe unbounded intervals

(-infinity, infinity)

(b)1 mark

What follows from this nonzero constant gradient?

Every input is a stationary point

Every primitive is a horizontal line

Decreasing linear primitives, with no stationary point

The primitive equals the constant gradient

(c)1 mark

Select the complete family of primitives. C is an arbitrary real constant

F(x)=-2+C

F(x)=2x+C

F(x)=-2x+C

F(x)=-2x

(d)1 mark

What is the degree of the primitive polynomial?

2

0

1

3