AP Calculus ABmediummcq1 pt

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

(-\infty, 0)

only

(0, 2)

only

(2, \infty)

only

(-\infty, 0)

and

(2, \infty)

Explanation

Core Concept

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

Correct Answer

B $(0, 2)$ only

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Practice Unit 5: Analytical Applications of Differentiation Questions →

Let g(x)=x4−4x3g(x) = x^4 - 4x^3g(x)=x4−4x3. On what open interval(s) is the graph of ggg concave down?

Explanation

Core Concept

Correct Answer

More Unit 5: Analytical Applications of Differentiation practice questions

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