Let f be a differentiable function on [a,b ] and x belongs to[a,b]. Show that, if f'(x)=0 and f''(x)>0, then f must have a local maximum at x.
Let f :[0,1] tends to R be a function defined by f(x)=x^m (1-x)^n, where m,n belongs to N.Find the values of m and n such that the Rolle’s Theorem holds for the function f .
Find the following limit x tends to 0 (1-cosx^2/x^2 - x^2 sin x^2)
Determine the local minimum and local maximum value of the function f defined by f(x)=3-5x^3+5x^4-x^5
If the nominal interest rate is 3%, how much is P5,000 worth in 10 years in a continuous compounded account?
Prove that a strictly decreasing function is always one-one
Find the following limit
Lim x tengs to 0 1-cos x^2/x^2 sin x^2
e) Evaluate lim x infty m 1+n^ 2 + m 4+n^ 2 + m 9+n^ 2 +***+ n 2n^ 2 ]