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Concave Upwards indicates Minima of the function i.

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If f x does not change sign as x increases through c, then c is neither a point of Local maxima nor a point of local minima. In fact, such a point is called point of inflection. Let f be twice differentiable at c. Then 1.

Then the value f c is local maximum value of f x. In this case, f c is local minimum value of f x. The graph gives a continuous function defined on a closed interval [a, d]. Also form the graph, it is evident that f has absolute maximum value f a and absolute minimum value f d.

Further note that absolute maximum minimum value of f x is different from local maximum minimum value of f x.

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The Laplace transform converts integral and differential equations into algebraic equations. It also converts time domain signal into frequency domain signal.

Inverse Laplace transform converts a frequency domain signal into time domain signal. Laplace Transforms Formulas The formulae given below are very useful to solve the many Laplace Transform based problems 1 Page.

Example Problems of Laplace Transforms Example 1: Initial value theorem is applicable only if the function is strictly proper function i.

Number of poles of X s is greater than the number of zeros of X s. Final value theorem is applicable only when the system is stable i.


If there are pairs of complex conjugate poles on the imaginary axis x t will contain sinusoidal components and final value is not defined. Liked this article on Laplace Transforms?

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