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When you solve for the 2nd derivative, you are determining whether the function is concave up/down. If you calculated that the 2nd derivative is negative, the function is concave down, which means you have a relative/absolute maximum, given that the 1st derivative equals 0.
To understand why this is, think about the definition of the 2nd derivative. It is a measure of the rate of change of the gradient. At a maximum, the gradient starts positive, becomes 0 at the maximum itself and then becomes negative, so it is decreasing. If the gradient is going down, then its rate of change, the 2nd derivative, must be negative.
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What is the anti derivative of negative sine?
The anti derivative of negative sine is cosine.
What is the derivative of negative sinx?
-cos(x)
What is the second derivative of square root x?
It is negative one divided by 4 multiplied by x to the power of 1.5 -1/(4(x^1.5))
What is the derivative value at an inflection point?
the second derivative at an inflectiion point is zero
What is the derivative of e negative x?
- e^- X
What to do when second derivative is equal to zero while calculating Maxima and Minima?
Plot the function. You may have found an inflection point.
What is the derivative of negative cosine?
The derivative of negative cosine is positive sine.
What is the anti derivative of negative sine?
The anti derivative of negative sine is cosine.
How do you trace a curve in differential calculus?
To trace a curve using differential calculus, you use the fact that the first derivative of the function is the slope of the curve, and the second derivative is the slope of the first derivative. What this means is that the zeros (roots) of the first derivative give the extrema (max or min) or an inflection point of the function. Evaluating the first derivative function at either side of the zero will tell you whether it is a min/max or inflection point (i.e. if the first derivative is negative on the left of the zero and positive on the right, then the curve has a negative slope, then a min, then a positive slope). The second derivative will tell you if the curve is concave up or concave down by evaluating if the second derivative function is positive or negative before and after extrema.
What is the geometrical meaning for second derivative?
The Geometrical meaning of the second derivative is the curvature of the function. If the function has zero second derivative it is straight or flat.
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 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 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 are the steps to solving an Optimization problem in calculus?
Optimization problems that involve finding the maxima or minima of functions also involve taking the first derivative of the function and finding locations where the value of the first derivative is equal to zero (by setting f'(x) = 0). The locations are either maxima, minima, or points of inflection and a second derivative test can be used to determine which of the three was found (max: f''(x) < 0, min: f''(x) > 0, PoI: f''(x) = 0).
Derivative of cosx?
The derivative of cos(x) is negative sin(x). Also, the derivative of sin(x) is cos(x).
f(x)= â x2fâ˛â˛(x)=?
The function given is (f(x) = -x^2). The second derivative of a function, denoted as (fâ'(x)), measures the concavity of the function. For the function (f(x) = -x^2), the first derivative (fâ(x)) is (-2x). Taking the derivative of (fâ(x)) gives us the second derivative (fââ(x)), which is (-2). So, (fâ'(x) = -2). This indicates that the function (f(x) = -x^2) is concave down for all (x), because the second derivative is negative.
What is the derivative of negative sinx?
-cos(x)
