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The derivative of a function is   an equation   a drawing   a function

The derivative of a function at a point is   an equation   a number   a function

The derivative is closely related to the following notion:   set of solutions of an equation   slope of a line   zero of a function

The derivative of a function  x → f(x)  measures   how steep its graph is   which value it takes for given x   where its graph intersects the axes

If  s(t)  is the position of a moving object at time  t, the derivative of the function  t → s(t)  is   the direction of the motion   the velocity   the acceleration

Let   f  be a differentiable function satisfying  f(3) = 5 and f '(3) = 2. An approximate value for  f(3.001)  is given by   5 × 0.001 = 0.005   5 + 2 × 0.001 = 5.002   2 + 0.001 = 2.001

If the derivative of a function is zero everywhere, the function must necessarily be   everywhere zero   constant   linear

A function is differentiable if its graph   undergoes no jumps   is part of a parabola   has no kinks and no points of infinite steepness

The notion of the derivative of a function  x → f(x)  provides an answer to the following question:

What is the content of the area under the graph?   How does the value of a function behave when x is changed a little bit?   Where does the graph intersect the x-axis?   How can a function be represented graphically?

 

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