From Derivative to Proportionality

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Description of Bottleneck

Students have difficulties to use derivative to calculate the change of function value. They believe the derivative is a magic transformation of one formula into another, e.g. x^2 into 2*x. They do not have an idea of Derivative=slope and change of Value=slope*change of argument

Desired learning outcome: given that f(1)=2 and f'(1)=3 the students should be able to make an estimation of f(1,01) as f(1)+f'(1)*0,01=2.003