Application of DerivativeMedium
Question
If the point (1,3) serves as the point of inflection of the curve y = ax3 + bx2 then the value of ′a′ and ′b′ are -
Options
A.a = 3/2 & b = - 9/2
B.a = 3/2 & b = 9/2
C.a = -3/2 & b = - 9/2
D.a = -3/2 & b = 9/2
Solution
y = ax3 + bx2
y′ = 3ax2 + b2x
y″ = 6ax + 2b
for point of inflection y″ = 0
x =
3a + b = 0 .... (i) (as x = 1)
point satisfy the curve also, so
3 = a + b .....(ii)
from (i) & (ii)
a = -
y′ = 3ax2 + b2x
y″ = 6ax + 2b
for point of inflection y″ = 0
x =
3a + b = 0 .... (i) (as x = 1)
point satisfy the curve also, so
3 = a + b .....(ii)
from (i) & (ii)
a = -
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