Polynomials and Derivatives

Master polynomial functions, roots, derivatives, differentiation rules, and optimization.

Questions

20, in 5 parts: Polynomial Functions and Degree · Concept of the Derivative · Trick Questions · Differentiation Rules · Applications: Extremes and Curves

Chapter

Analysis

Game

Citadel

Pack language

English

A taste of what is inside

1. In a real polynomial function f(x) = a_n × x^n + ... + a_0, what is the 'degree' of the polynomial?The highest exponent power of x with a non-zero coefficientThe sum of all coefficientsThe total number of terms in the polynomialThe value of the constant term a_0
2. Geometrically, the derivative f'(a) of a function at x = a represents the:Area under the curve from 0 to aLength of the curve at x = aSlope (gradient) of the tangent line to the graph at x = ay-intercept of the function
3. If the derivative f'(c) = 0 at a point, is x = c guaranteed to be a local maximum or minimum?No, derivatives cannot equal 0No, it can be an inflection pointYes, f'(c) = 0 guarantees a maxYes, f'(c) = 0 guarantees a min