Asked by Denzel

-x^4-3x^3+5x+6

Where does this function concave up and down?




Thanks for your help!!!
Answered by Reiny
Is it
y = -x^4 - 3x^2 + 5x + 6 ?

if so, take the second derivative.

if y '' is positive , the graph of the function is concave upwards

if y '' is negative , the graph of the function is concave downwards

Answered by Denzel
no its -x^4-3x^3+5x+6
Answered by Reiny
A function has to be written as an equation.

You just have an expression.
Is this not Calculus?
Answered by Denzel
its calculus its a webwork prob for my class
Answered by Reiny
Did you get
-12x^2 - 18x as your second derivative ?

critical values for this are
x = 0 and x = -3/2
( I set these equal to zero and solved)
You know the graph will be 'W"shaped downwards because of the -x^4.

consider the value of -12x^2 - 18x for x < -3/2
(try x = -5)
The expression will be negative, so
concave downwards for x < -3/2

consider the value of -12x^2 - 18x for x between -3/2 and 0
(try x = -1)
The expression will be -12(1) - 18(-1) which is positve,
so concave upwards for -3/2 < x < 0

I will let you decide what happens for x > 0
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