Application of Derivatives
Find the equation of the normal to curve x2=4ywhich passes through the point (1, 2).
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Prove that ∣∣tan−1x−tan−1y∣∣≤∣x−y∣∀x,y∈R˙
Show that between any two roots of e−x−cosx=0,
there exists at least one root of sinx−e−x=0
Discuss the extremum of f(x)=asecx+bcosecx,0<a<b
If the function f(x)=x3−6x2+ax+b
defined on [1,3] satisfies Rolles theorem for c=323+1
then find the value of aandb
be two differentiable functions in Randf(2)=8,g(2)=0,f(4)=10,andg(4)=8.
Then prove that gprime(x)=4fprime(x)
for at least one x∈(2,4)˙
If the function y=f(x) is represented as x=ϕ(t)=t5−5t3−20t+7,
then find the maximum and minimum values of y=f(x)˙
be the length of one of the equal sides of an isosceles triangle, and let θ
be the angle between them. If x
is increasing at the rate (1/12) m/h, and θ
is increasing at the rate of 180π
radius/h, then find the rate in m3
at which the area of the triangle is increasing when x=12mandthη=π/4.
Find the locus of point on the curve y2=4a(x+as∈ax)
where tangents are parallel to the axis of x˙