Examples:
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,..
Note 3:
d y and dy are not usually the same and dy is the approximate value of d y..
d y and dy are not usually the same and dy is the approximate value of d y..Example:
Find the approximate value of fourth root of 82 upto 3 decimal place..
Curve Sketching
The graph of a given function gives a visual presentation of the behaviour of the function involving a study of symmetry, rise and fall, region of existence, passage through specific points etc. The following points are helpful to trace the curv..
Example:
Sketch the curve y = - sin 2x ...
Passage through origin
Put x = 0, y = -sin2x = 0. This implies (0, 0) is a point on the curve or the curve passes through the origi..
Determination of Few Point
with this information, we sketch the graph as show ...
with this information, we sketch the graph as show ...Example:
Define The graph of the function is as follows: f(x) is increasing, because Since 2 - 1 < 3 - 1 (ii) f is said to strictly increasing in the interval I if For example, Let x 1 < x 2 f(x) is strictly increasing function. (iii) f(x) is said to be decreasing function if f..
Define The graph of the function is as follows: f(x) is increasing, because Since 2 - 1 < 3 - 1 (ii) f is said to strictly increasing in the interval I if For example, Let x 1 < x 2 f(x) is strictly increasing function. (iii) f(x) is said to be decreasing function if f..Working Rule to Check Whether a Differentable Function is Increasing or Decresing
(1) Let the given function be f (x) on the real number line R. (2) Differentiate the function f(x) with respect to x and equate it to zero i.e., put f '(x) = 0. Solve for x. These values of x which satisfy f '(x) = 0 are called Critical values of the function (3) Arrange these Critical values in a..
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