Derivative at a Point
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (..
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (..Derivability or Differentiability at a Point
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (a), then f | (a) is called the derivative or differential coefficient of f(x) at x = a. That ..
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (a), then f | (a) is called the derivative or differential coefficient of f(x) at x = a. That ..Interpretation of Derivative at a Point
Physical Significance: Let Q (t) be a quantity that changes with time 't'. Let D t be the increment given to 't' and D Q be the corresponding increment in Q, then is called the average rate of change of Q with respect to 't'. (Also known as Newton - quotient of f at t..
Physical Significance: Let Q (t) be a quantity that changes with time 't'. Let D t be the increment given to 't' and D Q be the corresponding increment in Q, then is called the average rate of change of Q with respect to 't'. (Also known as Newton - quotient of f at t..Derivative of a Function
So far we have discussed the derivative of a function f(x) at a point 'a' which is in the domain of f. Suppose we want to find the derivative of the same function at a different point 'b', then we have to compute the derivative by repeatin..
Application of Derivatives Conclusion
Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves. The h..
Conclusion - In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves. The h..Application of Derivatives Summary
x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x) such that A = (a , f(a)) and ..
x = a is called a point of inflexion. Rolle's theorem: If a function f(x) is such that (i) f (x) is continuous on [a,b] (ii) f (x) is differentiable on (a,b) and (iii) f (a) = f (b) Geometrical interpretation of Rolle's theorem Let AB be the graph of y = f(x) such that A = (a , f(a)) and ..Theorem 3: (Second Derivative Test)
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) ..
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) ..Points to Remember
Modes of reproduction in plants can be grouped into 2 types a) asexual b) sexual reproduction Regeneration of new plants from portions of vegetative organs is very common. Runner, rhizome, bulbs, corns and tubers serve as means of propagation. A population of genetically identical plants..
Derived Units
Derived Units - The units of all physical quantities can be derived from the seven basic units. These units are called derived units because they can be derived from the basic units algebraically by multiplication and division. It is frequently necessary to c..
Derived Units
The units of all physical quantities can be derived from the seven basic units. These units are called derived units because they can be derived from the basic units algebraically by multiplication and division. It is frequently necessary to convert one set of un..
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