A differentiable function has the following local tangent behaviors: • At

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

A differentiable function

f

has the following local tangent behaviors: • At

x = -2

, the tangent line slopes downward approximately

0.8

unit of

y

for each unit increase in

x

. • At

x = 0

, the tangent line is horizontal. • At

x = 3

, the tangent line slopes upward at about twice the steepness of the line

y = x

. Rank

f'(-2)

f'(0)

, and

f'(3)

from least to greatest.