What is the initial condition given for the function f?

Understanding Tangents and Differential Equations

Interactive Video
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Mathematics
•
9th - 12th Grade
•
Hard

Lucas Foster
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
f(1) = 1
f(0) = 0
f(-1) = -1
f(2) = 2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the y-intercept of the tangent line at any point P on the curve?
Twice the abscissa
The square of the abscissa
The cube of the abscissa
The abscissa itself
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the relationship between the slope of the tangent and the derivative of the function?
The slope is half the derivative
The slope is twice the derivative
The slope is the derivative
The slope is the square of the derivative
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What form does the differential equation take after simplification?
y' = y*x + x^2
y' = y*x - x^2
y' = y/x - x^2
y' = y/x + x^2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in solving the differential equation?
Assume a form for the solution
Differentiate both sides
Integrate both sides
Separate variables
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the assumed form of the solution for y?
Ax^2 + Bx + C
Ax^2 + Bx^3 + C
Ax^3 + Bx^2 + C
Ax^3 + Bx + C
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of A in the solution y = Ax^3 + Bx + C?
1/3
-1/2
1/2
-1/3
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