Application of Derivatives
Find all the points of local maxima and local minima of the function f given by f(x)=2x3−6x2+6x+5.
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Prove that all the point on the curve y=x+sinx
at which the tangent is parallel to x-axis lie on parabola.
Discuss the extremum of f(x)=x(x2−4)−31
are continuous functions in [a,b]
and are differentiable in(a,b)
then prove that there exists at least one c∈(a,b)
find the minimum possible number of roots of fprime(x)=0
Find the approximate value of(0.0037)21
Find the condition if f(x)
attains the minimum value only at one point.
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.
In the curve xm+n=am−ny2n
, prove that the mth
power of the sub-tangent varies as the nth
power of the sub-normal.