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```        at what points of the curve y=2/3x3+1/2x2 whose tangent makes equal angles with the co-ordinate axes is...................
plz explain
ANS=[1/2,5/24] and [-1,-1/6]```
6 years ago

30 Points
```										Dear Pranay,Solution:- y = 2/3 x3 + 1/2 x2...............(1)
Slope(m) = dy/dx =  2 x2 + x
Since tangent makes equal angles with the coord. axes, angle made by the tangent with positive x-axis can be either 450 or 1350. It means slope of tangent (m = tanΘ) can be either 1 (tan 450) or -1 (tan 1350).
Slope(m) = dy/dx =  2 x2 + x = 1 or -1
2  x2 + x - 1 = 0  or   2  x2 + x + 1 = 0
Since, 2  x2 + x + 1 = 0 has no real roots.
Therefore, 2  x2 + x - 1 = 0 which gives, x= -1 or 1/2.
Putting these values in eq. (1) will give y = -1/6 and 5/24 respectively.
Ans: [1/2,5/24] and [-1,-1/6]
Please feel free to post as many doubts on our discussion forum as you can. If you find any questionDifficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best Pranay!!!
```
6 years ago
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