Symmetry
a) Symmetry about x - axis If the equation of the curve remains unaltered when y is replaced by -y, then the curve is symmetrical about x-axis. b) Symmetry about y-axis If the equation of the curve remains unaltered when x is replaced by -x then the curve is symmetrical about y-axis. c) Symmetry a..
Solution:
Symmetry (a) By replacing y by -y, the equation (1) is altered, therefore the curve is not symmetrical about x-axis. (b) By replacing x by -x, the equation of the curve is altered, therefore the curve is not symmetrical about y-axis. (c) Replace x and y by -x and -y respectively in the equation y ..
Points of intersection
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 The tangent is paral..
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 The tangent is paral..Increasing and Decreasing Functions
This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. 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 ..
This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. 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 ..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..
Theorem 7:
Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b)...
Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b)...Note:
The value of c obtained need not be uniqu..
Step 2:
Find f '(x) and examine if it is defined at every point on the open interval (a, b). If f '(x) is defined for all x (a, b), then the function is differentiabl..
Find f '(x) and examine if it is defined at every point on the open interval (a, b). If f '(x) is defined for all x (a, b), then the function is differentiabl..Step 4:
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..
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..See what our Users say :
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