If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is:
If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the ordinate of the point which divides PQ internally in the ratio 1:2 is:
Option 1 -
0
Option 2 -
-t3
Option 3 -
-2t3
Option 4 -
2t3
-
1 Answer
-
Correct Option - 3
Detailed Solution:y = x3
Equation of tangent y – t3 = 3t2 (x – t)
Let again meet the curve at
=> t1 = -2t
Required ordinate =
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y (x) = 2x – x2
y? (x) = 2x log 2 – 2x
M = 3
N = 2
M + N = 5
Given f(X) =
So
put
(i) + (iii), f(x) +
Hence f(e) +
f' (x) = cosx + sinx − k ≤ 0∀x ∈ R
k ≥ √2
f (x) = x? /20 - x? /12 + 5
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Local maxima at 0, Local minima at 4/3
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x = 1 point of inflection
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