# Differential Equations: Change Your Euler Quiz

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) = x2 + 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).