# DERIVATIVE OF A FUNCTION 1.5. DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,

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DERIVATIVE OF A FUNCTION 1.5

DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,

DERIVATIVES ****THE DERIVATIVE IS A FUNCTION. IF YOU PLUG IN AN X VALUE, THE DERIVATIVE WILL TELL YOU THE SLOPE OF THE TANGENT LINE AT THAT X VALUE.

EXAMPLE 1 A)FIND THE DERIVATIVE: B)FIND THE SLOPE OF THE TANGENT LINE AT X=2

EXAMPLE 2 FIND DY/DX:

EXAMPLE

DIFFERENTIABILITY A FUNCTION IS DIFFERENTIABLE EVERYWHERE THAT THE DERIVATIVE EXISTS.

WHAT IT LOOKS LIKE TO NOT BE DIFFERENTIABLE AT A CORNER AT A CUSP AT A VERTICAL TANGENT AT A DISCONTINUITY

ONE SIDED DERIVATIVES SHOW THAT THE FOLLOWING FUNCTION IS NOT DIFFERENTIABLE AT X = 0

APPROXIMATE THE VALUE OF THE DERIVATIVE F(X) F’(1) F’(3) F’(2) F’(-1)

SKETCHING THE GRAPH GIVEN F(X) GRAPH F’(X)

HOMEWORK PG 144 #25, 26 ANSWER THE QUESTION AND APPROXIMATE THE VALUE OF F’(X1), F’(X7) PG 156 #1-31 ODD

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