SOLUTION: Consider the function f(x) = e^rx. Determine the values of r so that f sasisfies the equation f"(x) + f'(x)−6f(x) = 0. [

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Question 1049702: Consider the function f(x) = e^rx. Determine the values of r so that f sasisfies the equation f"(x) + f'(x)−6f(x) = 0.
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Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
Consider the function = . Determine the values of r so that f satisfies the equation f"(x) + f'(x)-6f(x) = 0
solution
f'(x)=
f"(x)=

f"(x) + f'(x)-6f(x) = 0
+-6=
*=
= and =
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=25 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2, -3. Here's your graph:


so
=
=
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