4:54 Professor could you please clear it a bit as if why cant a corner point be used to calc derivative? Cant we use limit and aporoximate from both sides using secants? It will be a great help. Nice explanation tho. Stuck on your channel fo months now!
we can’t find the derivative of a function at a corner in the graph, because the slope isn’t defined there :- since the slope to the left of the point is different than the slope to the right of the point. Therefore, a function isn’t differentiable at a corner
First, a correction f(x) has to be differentiable in (a,b), the curly brackets mean it can exclude a and b so just between them. Next, you should read japinder chaudhary's response to Pendulum below.
It’s indeed a good statement. Except for a small correction. If the function is not defined on xb, we can’t use it. But you can instead say differentiable on (a,b), has a right derivative at *a* and left derivative at *b* . Then it works fine
The if you know the slope of the secant line, you know f’(c) = that slope So just solve for c Example Function : x^2 + 3x + 2 Deriv: 2x + 3 Two points -1,0 and 0,2 The slope is 0-2 / -1-0 = 2 So we know f’(c) = 2 2c+ 3 = 2 2c= -1 c = -0.5 Which is correct since -0.5 is on the interval (-1, 0)
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4:54 Professor could you please clear it a bit as if why cant a corner point be used to calc derivative?
Cant we use limit and aporoximate from both sides using secants? It will be a great help.
Nice explanation tho. Stuck on your channel fo months now!
Are you still wondering?
we can’t find the derivative of a function at a corner in the graph, because the slope isn’t defined there :- since the slope to the left of the point is different than the slope to the right of the point. Therefore, a function isn’t differentiable at a corner
Amazing and helpful visuals. Thank you
Glad you liked it!
What if we only say that f(x) is differentiable in [a,b] then it will also be continuous in same.( Why do we have to specify both conditions?)
First, a correction f(x) has to be differentiable in (a,b), the curly brackets mean it can exclude a and b so just between them. Next, you should read japinder chaudhary's response to Pendulum below.
It’s indeed a good statement. Except for a small correction.
If the function is not defined on xb, we can’t use it.
But you can instead say differentiable on (a,b), has a right derivative at *a* and left derivative at *b* . Then it works fine
thank you sir....
Clutch
So how to find c?
The if you know the slope of the secant line, you know f’(c) = that slope
So just solve for c
Example
Function : x^2 + 3x + 2
Deriv: 2x + 3
Two points -1,0 and 0,2
The slope is 0-2 / -1-0 = 2
So we know f’(c) = 2
2c+ 3 = 2
2c= -1
c = -0.5
Which is correct since -0.5 is on the interval (-1, 0)
thank youuu!
Can you reply to my question? Why the secant or tangent line is called in this name? And how? Please reply!
Did you know why?
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