solving problems calculus 1

For a differentiable function f (x), find f '(x). Equate it to zero. Solve the equation f '(x) = 0 to get the Critical values of f (x..

If Mean value theorem is applicable, solve the equation Show that one of the roots lie in the open interval (a, b). This verifies the Mean Value Theore..

During the course of study of Mathematics, we must have come across several parts of inverse operations like (addition, subtraction) (multiplication, division) (forming an equation whose roots are given - solving a given equation) and so on. In practical situations, we may be interested t..

The points of intersection with x-axis is determined by letting y = 0. Putting y = 0, - sin 2x = 0 This implies the curve intersects the x-axis at the points where The points at which the tangent is parallel to x-axes are determined by solving. y = - sin 2x ..

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The different ways of solving differential equation are a follows:The different ways of solving differential equation are a follows: Method of separation of variables Homogeneous differential equations Linear differential equatio..

Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..

We know that every polynomial function is continuous and product of continues functions are continuous. f (x), being product of polynomials of degree 1, is a continuous function in [4,10..

Show the function f (x) is continuous on the closed interval [a, b..

Find all the points where f ' takes the value zer..