- #1
greg_rack
Gold Member
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- Homework Statement
- Given ##y=ax^3+bx^2+2x-3##, find the values of ##a## and ##b## for which the function has an horizontal inflection point at ##x=-1##.
- Relevant Equations
- none
For ##x=-1## to be an *horizontal* inflection point, the first derivative ##y'## in ##-1## must be zero; and this gives the first condition: ##a=\frac{2}{3}b##.
Now, I believe I should "use" the second derivative to obtain the second condition to solve the two-variables-system, but how?
Since it is an inflection point, shouldn't even the second derivative be zero? But the fact that it's an horizontal one is confusing me.
Now, I believe I should "use" the second derivative to obtain the second condition to solve the two-variables-system, but how?
Since it is an inflection point, shouldn't even the second derivative be zero? But the fact that it's an horizontal one is confusing me.