tough calculus problems

Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in measurement,..

1. If m = 0 the tangent at (x 1 , y 1 ) is parallel to x-axis. 2. If m 1 = m 2 the curves touch each other. 3. Rolle's theorem 4. Langrange's Mean Value theorem 5. Maxima and Mini..

Let (dy/dx) (x1,y1) = m be the slope of the tangent at (x1, y1) on the curve y=f(x). 1. Equation of the tangent at (x 1 ,y 1 ) is 2. Equation of the normal at (x 1 ,y 1 ) is..

Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..

Rolle's Theorem: Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b). ..

Let f be a function defined on an interval I and let x 1 and x 2 be any two points on I. (i) f is said to be increasing in the interval I, ..

Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..

dx and dy are called the differentials of x and y respectivel..

Let y = f (x) = x 1 / 4 Let x = 81, d x =1. Taking these values we have ..