Differentiability at a point for a piecewise function AP Calculus

#limits_calculus #calculusanilkumar #mcv4u_limits #IBSLcalculus #tangentsandnormals #limits_substitution #edexcel_limits #edexcel_calculus #limits_indeterminants

Continuity
The function f is continuous at x=c iff f(c) exists
lim┬(x→c)⁡〖f(x)〗 exists
lim┬(x→c)⁡〖f(x)〗=f(c)
Differentiability
The function f is differentiable at x=c if f'(c) has a numeric value
If f is differentiable at every value of x in an interval, then f is differentiable on that interval.
NOTE: The limits of f'(c) should exist for differentiability

[brsmovies]

Thank you. but how is (4-4)/h as h tends to 0 possible? i see it gives 0/0 which is undefined? let us dive into this again.
than you

[manvitkrishna]

I understand that some of u guys this sir is doing wrong or never seen that formulae ... Normally we use F(x)-f(a)/x-a and we solve it by subt.. But here it is the orginal formula which also give same result like normal but it will be long for values of x other than zero so i recommend u to follow sirs method for x=0 or normal one if x have other values

[lewisteya]

all I can comment may lord bless you you have assisted more students

[Meera-dzxr]

Sir i think, that you wrote wrong formula ..
The formula of LHD is f(a-h)-f(a)/-h..

[yogeshr]

Sir, Should we check differentiability for a derivative or for a function?

[vinuthasn]

U r explain graphically it is very helpful sir

[nicofe]

why in the left handed aproach f(a+h) is ((x+h)^2+4) instead of ((x^2+4)+h)?

[saihavish]

Sir for left hand derivative shouldn’t we take f(a-h)in place of f(a+h)

[TheHypercuts]

sir can we do by differentiating both the functions and putting the point where we have to check differentiability

[mohdhassan]

BUT you should first check that the function is continuous at x=0!!
for example if the second function in the piecewise is f(x)= 5 the whole function will satisfy your rules but it is not differentiable at x=5 because simply it is not continuous at that point.

[Sebastian-eq]

Wrong Ans : its not differentiable at x=0, since there is sharp corner at x=0!

[akmaths]

या तो स्क्रीन पर लिख लो या बोल लो, दोनों में से एक काम कर लो तो बहेतर होगा।
क्योंकि हम लोग हिंदी जानते है

[abhishekthakarn]

Hindi bolne chod do kya e karna bol ke ja ab english hai

[SKGamer-nhmy]

Sir, Kuch to Hindi bolo because all types students are here for teach mathematics 😊