Think you’ve got your head wrapped around **Differential Equations**? Put your knowledge to
the test. Good luck — the Stickman is counting on you!

Q. The line below has slope -1.5.

Determine the value of the missing number.

-3

8

14

There is insufficient information to answer this question.

Q. Determine the indicated value.

7

9

11

13

Q. If *f* (*x*) = *x*^{2} + 3, use a tangent line to *f* at *x* = 1 to estimate *f* (.75).

5

1.5

3.5

4.5

Q. The picture below shows the tangent line to *f* at *x* = 2:

Estimate *f* (2.1).

2.2

2.3

3.2

3.3

Q. Let *y* = *f* (*x*) be a solution to the initial value problem

Use a tangent line to approximate *f* (1.5).

3.5

4.5

Q. Let *y* = *f* (*x*) be a solution to the initial value problem

Use Euler's method with 2 steps to approximate *f* (3).

13.5

15.3

31.5

35.1

Q. Let *y* = *f* (*x*) be a solution to the initial value problem

Euler's method with more than one step is used to approximate *f* (2). Which of the following numbers is most likely to be the value found by the approximation?

0

7

8

9

Q. Let *f* (*x*) be a differentiable function defined for all real numbers, and let a be a real number. Which of the following statements is true?

If *f* is concave up and decreasing then the tangent line to *f* at *x* = a lies under the graph of *f*.

If *f* is concave up and decreasing then the tangent line to *f* at *x* = a lies over the graph of *f*.

If *f* is concave up and increasing then the tangent line to *f* at *x* = a lies over the graph of *f*.

If *f* is concave down except at *x* = a and *f* '(a) = 0 then the tangent line to *f* at *x* = a lies under the graph of *f*.

Q. If *y*(0) = 0 and , what is the error when Euler's method with 2 steps is used to approximate *y*(2)?

3

5

6

8

Q. Let *y* = *f* (*x*) be a solution to the initial value problem

Euler's method produces

an overestimate to the value *f* (1).

an underestimate to the value *f* (1).

the exact value *f* (1).

a formula for the solution *f* (*x*).