(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let g be a twice differentiable function with g'(x)>0 and g''(x)>0 for all real numbers x, such that g(4)=12 and g(5)=18. Of the following, which is a possible value for g(6)?

a. 15

b. 18

c. 21

d. 24

e. 27

Answer: e. 27

2. Relevant equations

3. The attempt at a solution

I guess the first question is the first line of the question. "Let g be a twice-differentiable function with g'(x)>0 and g''(x)>0" means the first and second derivative of g(x) is positive, right?

They gave me g(4)=12 and g(5)=18. Therefore, I can find the function by plugging it into y-y_{1}= m(x-x_{1}, find m, and then find b.

12-18 = m(4-5)

-6 = m(-1)

m=6

12 = 6(4) + b

b = -12

y= 6x-12

Since they want g(6), I plugged in 6 for x.

y= 6(6)-12

y= 24

Though that is answer d, it is incorrect.

I guess my problem might come from the first sentence. They told me g'(x) and g''(x) is positive, but I don't know how that helps me.

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# Homework Help: G(x) is twice differentiable where g(4)=12 and g(5)=18. g(6)=?

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