Using info from g' and g'' to find answer

[torquerotates]

Homework Statement

Let g be a twice differentiable function with g'(x)>0 and g''(x)>0 for all x.
g(4)=12 and g(5)=18. Which is a possible value for g(6)?

a)15
b)18
c)21
d)24
e)27

Homework Equations

slope=change y/ change x

The Attempt at a Solution

Ok so [g(5)-g(4)]/1=6
a-c is eliminated since they produce slopes less than 6. Since we know g''(x)>0. the slope must be increasing.

if g(6)=24 we get [g(6)-g(5)]/1=6. but this is a problem since the slope must be have increased from 4 to 5. So the answer is e) 27.

Is my reasoning correct?

 

[jedishrfu]

Yes, you got it.

As an analogy you could look at y=x^3, y'=3x^2 and y''=6x.