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There are lots of ways to proceed from here, but there's one simple, elegant solution.
You see that "tree" chart of derivatives Hero made? Once you've found a constant derivative, then you'll have a pattern. You can then trace the pattern backwards to extrapolate to find y for other values of x. That is, now that you have established the third derivative is a constant, you can now find values for y for values of x greater than 5 and less than 1. More specifically, you want to find the value of y when x=0.
Why? Not because it's a vertex or inflection point or anything fancy like that. There's a simpler reason. As Fit of Rage pointed out, the equation is of the form:
y = 2x^3 + (C/2)x^2 + Dx + E
At x=0, the first three terms of the polynomial are also equal to 0, meaning y=E. Now go on to the first derivative formula, substitute the values for y' at x=0 to solve for D, and so on.
You see that "tree" chart of derivatives Hero made? Once you've found a constant derivative, then you'll have a pattern. You can then trace the pattern backwards to extrapolate to find y for other values of x. That is, now that you have established the third derivative is a constant, you can now find values for y for values of x greater than 5 and less than 1. More specifically, you want to find the value of y when x=0.
Why? Not because it's a vertex or inflection point or anything fancy like that. There's a simpler reason. As Fit of Rage pointed out, the equation is of the form:
y = 2x^3 + (C/2)x^2 + Dx + E
At x=0, the first three terms of the polynomial are also equal to 0, meaning y=E. Now go on to the first derivative formula, substitute the values for y' at x=0 to solve for D, and so on.
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