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]

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 question
Difficult 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!!!

Approved