Application of Derivatives
Find the least value of a such that the function f given by f(x)=x2+ax+1is strictly increasing on (1,2)˙
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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___.
There is a point (p,q) on the graph of f(x)=x2
and a point (r,s)
on the graph of g(x)=x−8,wherep>0andr>0.
If the line through (p,q)and(r,s)
is also tangent to both the curves at these points, respectively, then the value of P+r
Find the approximate value of f(5.001),
Find the approximate value of (1.999)6
Prove that there exist exactly two non-similar isosceles triangles ABC
such that tanA+tanB+tanC=100.
Find the equations of the normal to the curve y=x3+2x+6
which are parallel to the line x+14y+4=0.
Find the range of the function f(x)=2x−2+4−x
If d is the minimum distance between the curves f(x)=exandg(x)=(log)ex, then the value of d6 is