Home > Calculus > Instantaneous Rate of Change at a Point

How do you find the instantaneous rate of change for #f(x)= x^3 +2x^2 + x# for [-1,2]?

Answer 1

Aurora Alvarado

Instantaneous rate of change :#f' (-1) = 0#

Start from the given #f(x) = x^3+ 2x^2+x# at #(-1, 2)#

#f' (x) = 3x^2+4x+1#

substitute #x=-1#

#f' (-1) = 3(-1)^2+4(-1)+1#

#f' (-1)= 0#

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Answer 2

Luke Alvarez

To find the instantaneous rate of change for ( f(x) = x^3 + 2x^2 + x ) on the interval ([-1, 2]), we first need to find the derivative of the function ( f(x) ), which represents the rate of change of the function at any given point. Then, we evaluate the derivative at the specific points within the interval to find the instantaneous rate of change at those points.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.