# How do you find the instantaneous rate of change of the function #x^3 +2x^2 + x# when x=1?

Apply the power rule to determine the function's derivative:

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To find the instantaneous rate of change of the function ( x^3 + 2x^2 + x ) when ( x = 1 ), you need to find the derivative of the function and then evaluate it at ( x = 1 ).

The derivative of the function ( f(x) = x^3 + 2x^2 + x ) is ( f'(x) = 3x^2 + 4x + 1 ).

Now, substitute ( x = 1 ) into the derivative function: [ f'(1) = 3(1)^2 + 4(1) + 1 = 3(1) + 4(1) + 1 = 3 + 4 + 1 = 8 ]

So, the instantaneous rate of change of the function ( x^3 + 2x^2 + x ) when ( x = 1 ) is ( 8 ).

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