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lude1
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Homework Statement
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
Homework Equations
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-y1 = m(x-x1, 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
-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
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.