Application of Derivatives
Find the values of x for which y=[x(x−2)]2is an increasing function
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)
If the tangent to the curve xy+ax+by=0 at (1,1) is inclined at an angle tan−12 with x-axis, then find aandb?
If f(x) is continuous in [a,b] and differentiable in (a,b), then prove that there exists at least one c∈(a,b) such that 3c2fprime(c)=b3−a3f(b)−f(a)