- #1
oowhitey
- 3
- 0
Homework Statement
find f''(x) <-- second derivative
f(x) = 3e^-x2 <-- that 2 is x squared
Homework Equations
The Attempt at a Solution
my attempt was 6x^2 e^x2
oowhitey said:Homework Statement
find f''(x) <-- second derivative
f(x) = 3e^-x2 <-- that 2 is x squared
The Attempt at a Solution
my attempt was 6x^2 e^x2
The second derivative of a function, denoted as f''(x), is the derivative of the first derivative of the function. It represents the rate of change of the slope of the function at a particular point.
The second derivative allows us to analyze the concavity of a function, which helps in identifying the maximum and minimum points of the function. It also helps in determining the nature of the graph, whether it is increasing or decreasing at a given point.
To find the second derivative of a function, you first need to find the first derivative of the function. Then, you apply the derivative rule again to the first derivative to get the second derivative. You can also use the quotient rule or the product rule to find the second derivative of more complex functions.
A positive second derivative indicates that the function is concave up, meaning it is increasing at an increasing rate. A negative second derivative indicates that the function is concave down, meaning it is decreasing at an increasing rate.
An inflection point is a point where the concavity of the function changes. To find the inflection points, we set the second derivative equal to 0 and solve for x. The resulting values represent the x-coordinates of the inflection points on the graph of the function.