Application of Derivatives
Find all points of local maxima and local minima of the function f given byf(x)=x3−3x+3.
Let f(x)andg(x) be differentiable function in (a,b), continuous at aandb,andg(x)=0 in [a,b]˙ Then prove that g(c)fprime(c)−f(c)gprime(c)g(a)f(b)−f(a)g(b)=(g(c))2(b−a)g(a)g(b)
A spherical iron ball 10cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/m∈ . When the thickness of ice is 5cm, then find the rate at which the thickness of ice decreases.
If fogoh(x) is an increasing function, then which of the following is not possible? (a)f(x),g(x),andh(x) are increasing (b)f(x)andg(x) are decreasing and h(x) is increasing (c)f(x),g(x),andh(x) are decreasing
Let f(x)andg(x) be two functions which are defined and differentiable for all x≥x0˙ If f(x0)=g(x0)andfprime(x)>gprime(x) for all x>x0, then prove that f(x)>g(x) for all x>x0˙
At the point P(a,an) on the graph of y=xn,(n∈N) , in the first quadrant, a normal is drawn. The normal intersects the y−aξs at the point (0,b) . If (lim)a0=21, then n equals _____.