Application of Derivatives
Find the intervals in which the function f given by f(x)=x3+x31,x=0is (i) increasing (ii) decreasing.
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Find the equation of the normal to the curve y=∣∣x2−∣∣x∣∣atx=−2.
In the curve xayb=Ka+b
, prove that the potion of the tangent intercepted between the coordinate axes is divided at its points of contact into segments which are in a constant ratio. (All the constants being positive).
Find the angle between the curves x2−3y2=a2andC2:xy3=c
radians, then find the approximate value of cos6001prime˙
Prove that f(x)=x−sinx
is an increasing function.
such that the length of the such-tangent and sub-normal is equal for the curve y=epx+px
at the point (0,1)˙
be a polynomial with real coefficients, Let a,b∈R,a<b,
be two consecutive roots of P(x)
. Show that there exists c
such that a≤c≤bandPprime(c)+100P(c)=0.
If the curve C
in the xy
plane has the equation x2+xy+y2=1,
then the fourth power of the greatest distance of a point on C
from the origin is___.