ryan.1015 said:well i found the derivative to be 10x^4 +30x^2+15 but when i graphed it i couldt figure out where it crossed the x axis
g(x)=2x^5-10x^3=15x-3.
ElectroPhysics said:I think from equating first derivative to zero u can easily find the point where no change occurs and beyond that it go on changing. and from 2nd derivative u can find the inflection points. Am I correct?
The purpose of finding these intervals is to understand the behavior and shape of a function. By identifying where a function is increasing or decreasing, we can determine the direction of change. Similarly, identifying concavity and inflection points can help us understand the curvature of a function and where it changes from being concave up to concave down or vice versa.
To find intervals of increasing and decreasing, you need to take the derivative of the function and set it equal to zero. Then, solve for the variable to find the critical points. The intervals between these critical points will be where the function is increasing or decreasing.
Concavity refers to the curvature of a function. A function can be concave up, where it curves upward like a cup, or concave down, where it curves downward like a frown. Inflection points are points where the concavity of a function changes, from concave up to concave down or vice versa.
To find intervals of concavity and inflection points, you need to take the second derivative of the function and set it equal to zero. Then, solve for the variable to find the inflection points. The intervals between these points will be where the concavity changes.
Identifying these intervals can help us understand the overall behavior of a function, which can be useful in various applications such as optimization, curve sketching, and understanding rates of change. It also allows us to locate critical points and inflection points which can help us find the maximum and minimum values of a function.