Application of Derivatives
The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.
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be differentiable function and g(x)
be twice differentiable function. Zeros of f(x),gprime(x)
, respectively, (a<b)˙
Show that there exists at least one root of equation fprime(x)gprime(x)+f(x)gx=0
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).
is differentiable function and iffprime(x)
does not vanish anywhere, then prove that f(−5)=f(5)˙
Discuss the extremum of f(x)=31(x+x1)
Discuss the global maxima and minima of f(x)∈[0,2]and(1,3)
and, hence, find the range of f(x)
for corresponding intervals.
If the tangent to the curve xy+ax+by=0
is inclined at an angle tan−12
with x-axis, then find aandb?
Two cyclists start from the junction of two perpendicular roads, there velocities being 3um/m∈
, respectively. Find the rate at which the two cyclists separate.