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Compare the right-hand and left-hand derivatives to show that the function is not differentiable. HW help?
Ok, so this is what the problem says:
Compare the right-hand and left-hand derivatives to show that the function is not differentiable at the indicated point ‘P.’ Support you findings graphically.
f(x) =
2, x<1
2x, x≥1
P=(1,2)
I don't think we can do anything with the 2.
for the 2x, the work would be like,
(1)(2)...since we drop one from exponent...and the answer would be two, but its not right.
Also, What am I supposed to do with P(1,2). I don't understand where that comes into play.
Thanks
If you look at the graph, you have a horizontal line from negative infinity to 1, and then it hits a corner and starts sloping upwards. You can't take the derivative of something at a corner like that, so it's not differentiable.
Now, algebraically, you're supposed to show that at the point (1,2), the derivative is not the same from both sides.
2 is a constant, and the derivative of a constant is 0, so the left hand derivative is 0.
The derivative of 2x is 2, so the right hand derivative is 2.
Now, the left hand derivative, 0, is not the same as the right hand derivative, 2. Though it is continuous, the function is not differentiable at the point (1,2).
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