How do you find the intervals where the

alahovom7ahc

alahovom7ahc

Answered question

2022-04-10

How do you find the intervals where the function f(x)=(2x12)(x3)2 is concave up and concave down?

Answer & Explanation

unduncjineei5r3

unduncjineei5r3

Beginner2022-04-11Added 19 answers

Step 1
Concave down in (,136) and concave up in (136,)
For finding the intervals where f(x) is concave up or concave down, first get f''(x).
f(x) is (2x1)(x3)2=2x313x2+24x9
f(x)=6x226x+24 and fx)=12x26. The inflection point is at x=136
Step 2
For x136, f''(x) is negative, hence f(x) would be concave down in the interval (,136)
For x136, f''(x) is positive, hence f(x) would be concave up in the interval (136,).

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