# Differential Equations: Change Your Euler Quiz

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!*

**Differential Equations**

Determine the value of the missing number.

*f*(

*x*) =

*x*

^{2}+ 3, use a tangent line to

*f*at

*x*= 1 to estimate

*f*(.75).

*f*at

*x*= 2:

Estimate *f* (2.1).

*y*=

*f*(

*x*) be a solution to the initial value problem

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

*y*=

*f*(

*x*) be a solution to the initial value problem

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

*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?

*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?

*f*is concave up and decreasing then the tangent line to

*f*at

*x*=

*a*lies under the graph of

*f*.

*f*is concave up and decreasing then the tangent line to

*f*at

*x*=

*a*lies over the graph of

*f*.

*f*is concave up and increasing then the tangent line to

*f*at

*x*=

*a*lies over the graph of

*f*.

*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*.

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

*y*(2)?

*y*=

*f*(

*x*) be a solution to the initial value problem

Euler's method produces

*f*(1).

*f*(1).

*f*(1).

*f*(

*x*).