Find the derivative of f(x) = 3 at x = 0 and at x=3
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Continuity and Differentiability of Special Functions
Redefine the given function according to the definition of special functions. As for example |2| = x if x > 0
|2| = -x if x < 0
1. Observe the points where the given function can be non-differentiable. 2. Check right hand limit Derivative and left hand derivative at those points. 3. If LHD = RHD ,the function is differentiable at those points. 4. If LHD + RHD ,the function is not differentiable at those points.
Theorems on Differentiability
If f(x) and g(x) are both derivable at x = a , f(x) = g(x),f(x). g(x) and f(x) g(2) will also be derivable at x = a.
If both f(x) and g(x) are non derivable then nothing can be said about the sum /difference /product function. if f(x) is derivable at x = a and f(a) = 0 and g() is continuous at x = a
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