Sec 2.8: THE DERIVATIVE AS A FUNCTION replace a by x

Sec 2.8: THE DERIVATIVE AS A FUNCTION Slopes : 0 + -

Sec 2.8: THE DERIVATIVE AS A FUNCTION

Definition: A function f is differentiable on an open interval (a, b) if it is differentiable at every number in the interval. Definition: A function f is differentiable on an open interval (a, b) if it is differentiable at every number in the interval.

Sec 2.8: THE DERIVATIVE AS A FUNCTION 2 properties continuity differentiability Proof: Remark: f cont. at af diff. at a Remark: f discont. at af not diff. at a Remark: f discont. at a f not diff. at a

Sec 2.8: THE DERIVATIVE AS A FUNCTION Example: f cont. at af diff. at a f discont. at af not diff. at a f discont. at a f not diff. at a

Sec 2.8: THE DERIVATIVE AS A FUNCTION Example: f cont. at af diff. at a f discont. at af not diff. at a f discont. at a f not diff. at a

Sec 2.8: THE DERIVATIVE AS A FUNCTION HOW CAN A FUNCTION FAIL TO BE DIFFERENTIABLE?

Sec 2.8: THE DERIVATIVE AS A FUNCTION Higher Derivative Note: jerk acceleration velocity

MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag R

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