The following table gives values of the differentiable function y = f ( x ) . Es

Q: The following table gives values of the differentiable function y = f ( x ) . Es

local max at x=2,7 local min at x=5 Now assuming it to be table for f'(x) Now critical points are those at which f'(x)=0 So critical points between x=0&1,2&3,6&7,8&9 local max at the pt. between 2&3,8&9 {as sign of f' changes from + to -} local min at the pt. between 0&1,6&7 {as sign of f' changes from - to +} This is the first derivative test. as sign change means a continuous fuction will cross the value 0

ID: 2841433 • Letter: T

Question

The following table gives values of the differentiable function y=f(x).

Estimate the x-values of critical points of f(x) on the interval 0<x<10. Classify each critical point as a local maximum, local minimum, or neither.

critical points and classifications: (2,max),(5,min),(7,max)

Now assume that the table gives values of the continuous function y=f?(x) (instead of f(x)). Estimate and classify critical points of the function f(x).

critical points and classifications:

x 0 1 2 3 4 5 6 7 8 9 10 y -1 2 3 -1 -3 -5 -4 2 1 -2 -4

Explanation / Answer

local max at x=2,7

local min at x=5

Now assuming it to be table for f'(x)

Now critical points are those at which f'(x)=0

critical points between x=0&1,2&3,6&7,8&9

local max at the pt. between 2&3,8&9 {as sign of f' changes from + to -}

local min at the pt. between 0&1,6&7 {as sign of f' changes from - to +}

This is the first derivative test.

as sign change means a continuous fuction will cross the value 0

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The following table gives values of the differentiable function y = f ( x ) . Es

The following table gives values of the differentiable function y=f(x). x 0 1 2

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The following table gives values of the differentiable function y = f ( x ) . Es

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