Calculus 1000A/B Lecture 11: September 26 Notes
17 Oct 2018
School
Department
Course
Professor
CALCULUS 1000 CLASS NOTES
Wednesday, September 26, 2018
Session 011
Allen O’Hara
Ex. Take the derivative of
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= 3
Ex. Find the derivative of
f’(x) =
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=
=
=
=
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= (slope of tangent to at (0,1))
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Ex. Find the derivative of
f’(x) =
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= f’(0) (slope of tangent to y = at (0,1)
Ex. Find the derivative of f(x) = at 0
f’(0) =
=
= DNE
RECALL
‘e’ is defined so slope of
tangent at (0,1) is 1
f’(0) = 1
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CALC 1000A/B Full Course Notes
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Document Summary
Find the derivative of (cid:2187) f(cid:859)(cid:894)(cid:454)(cid:895) = lm (cid:2868)(cid:3033)(cid:4666)(cid:3051)+ (cid:4667) (cid:3033)(cid:4666)(cid:3051)(cid:4667) = (cid:1857)(cid:3051)(cid:1858) (cid:4666)(cid:4667) (slope of tangent to (cid:1857)(cid:3051) at (0,1)) = (cid:3051) f(cid:859)(cid:894)(cid:1004)(cid:895) (slope of tangent to y = (cid:3051) at (0,1) Find the derivative of f(x) = || at 0 f(cid:859)(cid:894)(cid:1004)(cid:895) = lm (cid:2868)|(cid:2868)+ | |(cid:2868)| Recall (cid:858)e(cid:859) is defined so slope of tangent at (0,1) is 1. Left side: lm (cid:2868) | | = lm (cid:2868) = lm (cid:2868) (cid:883) = -1. Ride side: lm (cid:2868)+| | = lm (cid:2868)+ = lm (cid:2868) (cid:883) = 1. If f(x) is differentiable at a, f(x) is continuous at a. If f(x) is continuous at a, does not mean f(x) is differentiable at a: at peaks or cusps. Notation for derivatives: (cid:862)let f(cid:894)(cid:454)(cid:895) e(cid:395)ual _____ find the de(cid:396)i(cid:448)ati(cid:448)e(cid:863) [(cid:2870) (cid:885)+(cid:886)](cid:859) = : (cid:3031)(cid:3052)(cid:3031)(cid:3051)|(cid:3051)=(cid:3028, (cid:3031)(cid:3031)(cid:3051)(cid:1858)(cid:4666)(cid:4667)|(cid:3028) f(cid:859)(cid:894)(cid:454)(cid:895) = lm (cid:2868)(cid:3033)(cid:4666)(cid:3051)+ (cid:4667) (cid:3033)(cid:4666)(cid:3051)(cid:4667) [f(cid:894)(cid:454)(cid:895)+g(cid:894)(cid:454)(cid:895)](cid:859) = [f(cid:894)(cid:454)(cid:895)](cid:859) + [g(cid:894)(cid:454)(cid:895)](cid:859: assuming f(x) and g(x) are differentiable.
