calculus 3 problems

Differentiate y = (x+2) (x+3) by using the formul..

d y and dy are not usually the same and dy is the approximate value of d y..

Check the sign of f'(x) in the immediate neighbourhood of each critical valu..

Check if f (a) = f (b) If all the above condition are satisfied, then Rolle's theorem is applicable else the Rolle's theorem is not applicable. If Rolle's theorem is applicable, solve f '(c) = 0. Show that one of these roots lie in the open interval (a, b..

If f (a) and f (b) are opposite in sign then the curve crosses the x-axis say at c. Then the area bounded the curve f (x), x-axis and the ordinates x = a and x = b is ..

Every polynomial function is continuou..

Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 and f "(a) = 0. In this case we..

Differentiate cos - 1 (2x+3) from first principle..