Apentix/AP Calculus AB/Unit 5: Analytical Applications of Differentiation/Question
AP Calculus ABmediummcq1 pt

Let g(x)=x4−4x3g(x) = x^4 - 4x^3. On what open interval(s) is the graph of gg concave down?

Explanation

Core Concept

Correct. The second derivative is g′′(x)=12x2−24x=12x(x−2)g''(x) = 12x^2 - 24x = 12x(x - 2). Setting g′′(x)<0g''(x) < 0 yields 0<x<20 < x < 2, which corresponds to the graph being concave down.

Correct Answer

q6_b

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