Answer :
Final answer:
To locate transition points such as points of inflection and local minimums for the function y = 5x^6 - 45x^4, calculate and analyze the first and second derivatives, then solve for x at critical points where derivatives are zero or change signs.
Explanation:
To find the transition points, such as points of inflection and local minimums, of the function y = 5x6 - 45x4, you need to perform calculus operations like differentiation and identify the critical points.
Points of Inflection
To find the points of inflection, calculate the second derivative y'' of the function and set it equal to zero. Then solve for x to determine the points where the concavity of the function changes. Remember, a point of inflection occurs where the second derivative changes sign.
Local Minimum
To find the local minimum, you first need to find the first derivative y' of the function and identify the critical points by setting y' equal to zero and solving for x. Then use the second derivative test or analyze the sign changes of the first derivative to confirm whether these critical points are local minima.
