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let f be a function and f' the first derivative.
- If f'>0 the function is genuinely ascending.
- If f'<0 the function is genuinely descending.
- If f'>=0 the function is ascending.
- If f'<=0 the function is descending.
- If f'=0 the function is stable.
What else can I help you with?
How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
What is the derivative of x to the second power?
2x is the first derivative of x2.
Does The second derivative represent the rate of change of the first derivative?
Yes.
What is the derivative of x to the second powerr?
2x is the first derivative of x2.
How do you find the second derivative?
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
What is the first derivative of speed?
Speed is scalar (it doesn't have direction), and the magnitude of velocity (a vector). The first derivative of velocity is acceleration, therefore the first derivative of speed is the magnitude of acceleration.
What is the second derivative of a function's indefinite integral?
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.
What is the geometrical meaning of second derivative?
The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.
What is the physical application of third- and fourth-order derivatives with respect to distance e g first derivative is slope?
in case of derivative w.r.t time first derivative with a variable x gives velocity second derivative gives acceleration thid derivative gives jerk
What is the function if the first derivative of a function is a constant?
A linear function, for example y(x) = ax + b has the first derivative a.
What is the first derivative of e raised to the power of x?
The first derivative of e to the x power is e to the power of x.
What is the second derivitive of sec x?
Write sec x as a function of sines and cosines (in this case, sec x = 1 / cos x). Then use the division formula to take the first derivative. Take the derivative of the first derivative to get the second derivative. Reminder: the derivative of sin x is cos x; the derivative of cos x is - sin x.
