How many points of inflection are on the graph of the function?
f(x)=18x^3+5x^2-12x-17
f(x)=18x^3+5x^2-12x-17
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Take the 2nd derivative, set it to 0, solve for x
f(x) = 18x^3 + 5x^2 - 12x - 17
f'(x) = 54x^2 + 10x - 12
f''(x) = 108x + 10
f''(x) = 0
0 = 108x + 10
108x = -10
54x = -5
x = -5/54
1 inflection point
f(x) = 18x^3 + 5x^2 - 12x - 17
f'(x) = 54x^2 + 10x - 12
f''(x) = 108x + 10
f''(x) = 0
0 = 108x + 10
108x = -10
54x = -5
x = -5/54
1 inflection point
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Just one.
Plot it on MS Excel. U will get a curve with. At (0,0) slop of curve is "zero" and before and after that function shows the same trend(that is increasing). Which is the definition of "inflection".
Plot it on MS Excel. U will get a curve with. At (0,0) slop of curve is "zero" and before and after that function shows the same trend(that is increasing). Which is the definition of "inflection".
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A point of inflection requires f"(x)=0. Since f(x) is cubic f '(x) is quadratic and f "(x) is linear
so there is just one point of inflection. You should now be able to find it!
so there is just one point of inflection. You should now be able to find it!
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Here, order of polynomial(n)=3
=> points of inflection =3 Ans.
=> points of inflection =3 Ans.