Application of DerivativeHard
Question
If there are exactly two different tangents are possible to the curve f(x) = x4 + αx3 + βx which pass through origin, then -
Options
A.α > 0, β ∈ R
B.α < 0, β ∈ R
C.α ∈ R, β > 0
D.α ∈ R, β ∈ R
Solution
∴ jmop = 
⇒
= 4h3 + 3αh2 + β
⇒ h4 + αh3 + βh = 4h4 + 3αh3 + βh 3h4 + 2αh3 = 0
⇒ h3(3h + 2α) = 0 ⇒ h = 0, h = -
⇒ α ≠ 0 and β ∈ R
for two different values of h.
⇒
= 4h3 + 3αh2 + β⇒ h4 + αh3 + βh = 4h4 + 3αh3 + βh 3h4 + 2αh3 = 0
⇒ h3(3h + 2α) = 0 ⇒ h = 0, h = -
⇒ α ≠ 0 and β ∈ R
for two different values of h.
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