Application of Derivatives
Find the intervals in which the function f given by f(x)=x2−4x+6is (a) strictly increasing (b) strictly decreasing
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The graph y=2x3−4x+2andy=x3+2x−1
intersect in exactly 3 distinct points. Then find the slope of the line passing through two of these points.
of a particle at time t
is expressed as s=21t3−6t˙
Find the acceleration at the time when the velocity vanishes (i.e., velocity tends to zero).
For the curve y=4x3−2x5,find all the points at which the tangent passes through the origin.
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)˙
The two curves x3−3xy2+2=0 and 3x2y−y3−2=0
Find the equation of the tangent to the curve (1+x2)y=2−x,
where it crosses the x-axis.
Find the distance of the point on y=x4+3x2+2x
which is nearest to the line y=2x−1
find the minimum possible number of roots of fprime(x)=0