Question

do the functions have the same concavity?
$f(x)=4x^{2}-108$
$y = g(x)$
choose 1 answer:

Explanation:

Step1: Find the second - derivative of \(f(x)\)

First, find the first - derivative of \(f(x)=4x^{2}-108\). Using the power rule \((x^n)^\prime=nx^{n - 1}\), \(f^\prime(x)=(4x^{2}-108)^\prime = 8x\). Then find the second - derivative \(f^{\prime\prime}(x)=(8x)^\prime=8>0\). So \(f(x)\) is concave up.

Step2: Analyze the graph of \(y = g(x)\)

The graph of \(y = g(x)\) is a parabola opening downwards. A parabola opening downwards is concave down.

Answer:

No