Question

Which correctly describes the concavity of the function
f(x) = x^3 – 5x + 7?
Whixh is true?
concave upward in the interval (-3, 0)
concave downward in the interval (0, 3)
concave upward in the interval (0, 3)
concave downward in the interval (-3, 3)

Answer 1

take second derivative
f'(x)=3x^2 -5
f''(x)= 6x
6x=0
x=0
that's means point of inflection is at 0(point were concavity changes), positive x value has up concavity, while negative value have down concavity.

Let's look at the graph
http://www.wolframalpha.com/input/?i=x^3%20%E2%80%93%205x%20%2B%207&t=crmtb01

Answer 2

What does that tell me?

Answer 3

Do i plug in all the x values for 6x?

Answer 4

If you plug in negative number for x in 6x, you get a negative; if you plug in positive, you get positive

Answer 5

So.. concave downward in the interval (-3, 3) is the correct answer :D

Answer 6

no, concave upward in the interval (0, 3)

Answer 7

how?

Answer 8

look at the graph

Answer 9

choose a number in the interval (0,3) like 1
6(1) is positive which means it is concave up

Answer 10

ohhh okay tanks (:

Answer 11

we know concave down on interval (-3,3) would be wrong since 0 is an inflection point (which means the convaity switches)
see:
6(-1)=- which means concave down before 0
6(1)=+ which means concave up after 0