Application of Derivatives
If in a triangle ABC,
the side c
and the angle C
remain constant, while the remaining elements are changed slightly, show that
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Discuss the maxima and minima of the function f(x)=x32−x34˙
Draw the graph of y=f(x)
and find the range of f(x)˙
is continuous in [a,b]
and differentiable in (a,b), then prove that there exists at least one c∈(a,b)
If a>b>0, with the aid of Lagranges mean value theorem, prove that nbn−1(a−b)1.
The tangent at any point on the curve x=acos3θ,y=asin3θ
meets the axes in PandQ
. Prove that the locus of the midpoint of PQ
is a circle.
Discuss the extremum of f(x)=x(x2−4)−31
For the curve y=a1n(x2−a2)
, show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.
Discuss the extremum of
For the curve xy=c,
prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.