- #1
diye
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how would I find the first and second derivative of
(x^3/3) - 2x^2 + 3x +8
thanks
(x^3/3) - 2x^2 + 3x +8
thanks
You have too much stuff.diye said:f(x) = x^3/3-2x^2 + 3x +8
first derivative: x^2 - 4x + 3 ... x = 3 x = 1
second derivative: 2x - 4 ... x = 2
diye said:s(0) = 8
s(1) = 9 1/3
s(2) = 8 2/3
s(3) = 8
so now
time | velocity | acceleration | speed
0 < x <1
1< x < 2
2< x < 3
x> 3
how would I find out the velocity acceleration speed?
The first and second derivative are used to calculate the rate of change and the curvature of a function, respectively. They are important tools in understanding the behavior of a function and can be used to solve various optimization problems.
To find the first derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule. These rules involve taking the derivative of each term in the function and combining them using algebraic operations.
The first derivative tells us about the slope of the function at a specific point. It can also be used to determine whether the function is increasing or decreasing at that point, as well as the location of any maximum or minimum points.
The second derivative can be found by taking the derivative of the first derivative. In other words, you can apply the same rules used to find the first derivative to the first derivative itself. The resulting second derivative can tell us about the concavity and inflection points of the function.
The second derivative is important in calculus as it provides information about the rate of change of the slope (or the curvature) of a function. It can be used to determine the concavity of a function, which is crucial in optimization problems. Additionally, the second derivative test can be used to find the nature of a critical point, whether it is a minimum, maximum, or inflection point.