
Differential Equations and Exponential Functions
Interactive Video
•
Mathematics, Science
•
10th - 12th Grade
•
Practice Problem
•
Hard
Amelia Wright
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main goal of the problem discussed in the video?
To integrate an exponential function
To find the derivative of an exponential function
To solve a quadratic equation
To find values of K for which the exponential function is a solution to a differential equation
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which mathematical rule is applied to find the derivative of the exponential function?
Product Rule
Quotient Rule
Power Rule
Chain Rule
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first derivative of the function y(x) = e^(kx)?
e^(kx)
k * e^(kx)
k^2 * e^(kx)
e^(k)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the second derivative of the function y(x) = e^(kx)?
k^3 * e^(kx)
e^(kx)
k^2 * e^(kx)
k * e^(kx)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step after finding the derivatives in solving the differential equation?
Graph the function
Integrate the function
Substitute the derivatives into the differential equation
Solve for y
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What common factor is factored out from the expression during simplification?
k
k^2
e^(kx)
8
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the factors of the trinomial k^2 - 6k + 8?
(k - 4)(k - 2)
(k + 4)(k + 2)
(k - 3)(k - 3)
(k + 4)(k - 2)
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