Question 145705: Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x.
f(x) = x2 + 5x + 6
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! f(1)=1+5+6=12
f(2)=4+10+6=20
f(4)=16+20+6=42
f(8)=64+40+6=110
f(16)=256+80+6=342
From calculus we will know that the slope is given by f'(x)=2x+5. That is to say, each increase in x results in a growing increase in y, and it grows at the aforementioned rate.
Also, note the differences between values.
8->22->68->232, the differences are growing larger by each increase in x.
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