What x values is the function concave down

Nikhil Holt

Nikhil Holt

Answered question

2022-03-14

What x values is the function concave down if
f(x)=15x23+5x?

Answer & Explanation

orangepaperiz7

orangepaperiz7

Beginner2022-03-15Added 9 answers

Step 1
f(x)=15x23+5x is concave downward for all x<0
As Kim suggested a graph should make this apparent (See bottom of this post).
Alternately,
Note that f(0)=0
and checking for critical points by taking the derivative and setting to 0
we get
f(x)=10x13+5=0
or
10x13=-5
which simplifies (if x<>0) to
x13=2
x=8
At x=8
f(8)=15(8)23+5(8)
=15(2)2+(40)
Since (8, 20) is the only critical point (other than (0, 0) ) and f(x) decreases from x=8 to x=0
it follows that f(x) decreses on each side of (8, 20), so
f(x) is concave downward when x<0
When x>0 we simplify note that
g(x)=5x is a straight line and
f(x)=15x23+5x remains a positive amount (namely 15x23 above that line therefore f(x) iss not concave downward for x>0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?