Application of Derivatives
Let f(x) be a polynomial of degree four having extreme values at x=1and x=2. If (lim)x0[1+x2f(x)]=3, then f(2) is equal to :
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If φ(x) is differentiable function ∀x∈R and a∈R+ such that φ(0)=φ(2a),φ(a)=φ(3a)andφ(0)=φ(a) then show that there is at least one root of equation φprime(x+a)=φprime(x)∈(0,2a)
Find the possible values of p
such that the equation px2=(log)ex
has exactly one solution.
are angles satisfying 0<α<θ<β<2π˙
Then prove that
Find the condition if f(x)
attains the minimum value only at one point.
The curve f(x)=x−10x2+ax+6
has a stationary point at (4,1)
. Find the values of aandb
. Also, show that f(x)
has point of maxima at this point.
If the slope of line through the origin which is tangent to the curve y=x3+x+16
then the value of m−4
A regular square based pyramid is inscribed in a sphere of given radius R
so that all vertices of the pyramid belong to the sphere. Find the greatest value of the volume of the pyramid.
For the curve xy=c,
prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.