Application of Derivatives
Find the maximum and minimum values, if any, of the following functions given by
Discuss the extremum of f(x)=2x3−3x2−12x+5 for x∈[−2,4] and the find the range of f(x) for the given interval.
Two towns AandB are 60 km apart. A school is to be built to serve 150 students in town Aand50 students in town B˙ If the total distance to be travelled by 200 students is to be as small as possible, then the school should be built at (a)town B (b)town A (c)45 km from town A (d)45 km from town B
For the curve y=a1n(x2−a2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.
Let f defined on [0,1] be twice differentiable such that ∣f(x)∣≤1 for x∈[0,1]. if f(0)=f(1) then show that ∣f′(x)<1 for all x∈[0,1].