TG EAMCET 2 May 2025 Shift 1 Paper

Given, curve y=x3−2x2+3x−2
So, slope of tangent, m=‌

dy

dx

=3x2−4x+3
Now, the rate of change of the slope of tangent = second derivative ‌

d2y

dx2

⇒‌‌‌

d

dx

(3x2−4x+3)=6x−4
At point (2,4),
‌

d2y

dx2

=6×2−4=8
Now, the abscissa is x. So, the rate of change of the abscissa is ‌

dx

dt

Now, given ‌

d

dt

(‌

dy

dx

)=k‌

dx

dt

‌⇒‌‌‌

d2y

dx2

⋅‌

dx

dt

=k‌

dx

dt

⇒‌

d2y

dx2

=k
‌⇒‌‌k=8‌‌‌ [using Eq. (i)] ‌