IB Mathematics Applications & Interpretation Topic…

The slope field for $\frac{d y}{d x}=x y$ , for $-2 \leq x \leq 2,-2 \leq y \leq 2$ , is shown below. The green curve should be ignored; the point $A(2,-1)$ is marked.

Write down the equations of the curves where $\frac{d y}{d x}=0$ .

Consider the differential equation $\frac{d y}{d x}=e^{x}-y$ , for .

The slope field for $\frac{d y}{d x}=x^{2}-y^{2}$ , for , is shown below.

Consider the differential equation $\frac{d y}{d x}=\sin (y)-x$ , for .

A slope field for $\frac{d y}{d x}=x^{2}-y^{2}$ on is displayed here.

the lines $x=0$ and $y=0$ on the slope field.

the solution curve passing through $A(2,-1)$ .

the concavity at $A(2,-1)$ of the solution curve from Part 2.

$\frac{d y}{d x}$ at $(0,1)$ .

Find the equation of the curve where the slope is zero.

the coordinates of the point where the solution curve through $(0,1)$ intersects the curve from Part 1.

Find the equation of the tangent line to the solution curve through $(0,1)$ at the intersection point found in Part 2.

Find the equations of the curves where $\frac{d y}{d x}=0$ .

the curves from part 0 on the slope field.

the solution curve passing through $(0,1)$ .

whether the solution curve from part 2 has any turning points in $-2\le x\le 2$ . your answer.

Write down the value of $\frac{d y}{d x}$ at the point $\left(0, \frac{\pi}{2}\right)$ .

Find the curve where $\frac{d y}{d x}=0$ .

the nature of the points on the curve found in Part 1 (e.g., maximum, minimum, or neither).

Find the equations of the curves on which $\frac{d y}{d x}=0$ .

the curves obtained in part 0 on the slope field.

the solution curve that goes through $(0,-1)$ .

whether the solution curve from part 2 has any turning points in $-\frac{1}{2}\le x\le \frac{1}{2}$ . your answer.

IB Mathematics Applications & Interpretation AHL 5.15—slope Fields Questionbank

IB Mathematics Applications & Interpretation AHL 5.15—slope Fields Questionbank

IB Mathematics Applications & Interpretation AHL 5.15—slope Fields Questionbank

IB Mathematics Applications & Interpretation AHL 5.15—slope Fields Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 5.15—slope Fields Questionbank