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

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]

Grade:12

1 Answers

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
10 years ago

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]


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