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Assuming function of one variable...
Want y[x] s.t. y''[x] =y[x]
The characteristic equation is r^2 = 1.
r = (+/-) 1
So, e^(x*1) and e^(x * -1) work. To get full generality, multiply them by any constants A,B and add.
y[x] = A e^x + B e ^(-x)
y'[x] = A e^x - B e ^(-x)
y''[x] = A e^x + B e ^(-x) = y[x]
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How can you know that a value is the minimum of a function?
When the first derivative of the function is equal to zero and the second derivative is positive.
To find critical points?
Take the derivative of the function and set it equal to zero. The solution(s) are your critical points.
What is a derivative graph?
A derivative graph tracks the slope of a function.
What is the name for values of an independent variable for a function that make its derivative equal to 0 or not defined but are not within the domain of the original function?
That sounds a lot like a critical point to me.
What is the derivative of 3cosx?
The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).
