Application of Derivatives Mind Map

If y is a function of x, then dy/dx gives the instantaneous rate of change of y with respect to x at a given value of x.

Write the relation between quantities first, differentiate both sides with respect to time or the given independent variable, then substitute values with units.

A function f is increasing on an interval when larger x-values give larger function values, and decreasing when larger x-values give smaller function values.

Make a derivative sign table using critical points; do not decide monotonicity from one random value unless it represents the whole interval.

A function has a local maximum at a point if its value is greater than or equal to nearby values, and a local minimum if its value is less than or equal to nearby values.

After finding a critical point, always apply a test and state both the point and the value if asked.

The absolute maximum and absolute minimum of a continuous function on a closed interval are the greatest and least function values attained on that interval.

Create a value table with endpoints and valid critical points; comparison of f-values earns the final decision.

Optimisation uses derivatives to find the maximum or minimum value of a quantity under given conditions or constraints.

Define variables clearly and mention the feasible domain, such as positive length, positive radius, or dimensions within the given constraint.