Application of Derivatives
What is the maximum value of the function sinx+cosx?
Let f(x)=2x3=9x2+12x+6. 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 function y=f(x) is represented as x=ϕ(t)=t5−5t3−20t+7, y=ψ(t)=4t3−3t2−18t+3(∣t∣<2), then find the maximum and minimum values of y=f(x)˙
The lateral edge of a regular rectangular pyramid is acmlong˙ The lateral edge makes an angle α with the plane of the base. Find the value of α for which the volume of the pyramid is greatest.
If a>b>0, with the aid of Lagranges mean value theorem, prove that nbn−1(a−b)1. nbn−1(a−b)>an−bn>nan−1(a−b),if0<n<1.