How do I tell if the statement the marginal rate of change of the function f(x)=x^5 at the point (2,32) is 80 is true or false?

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You need to evaluate the rate of change of function `f(x),`  thus, you need to find the slope of the tangent line to the function f(x), at the point `(2,32), ` hence, you should differentiate the function with respect to x, such that:

`f'(x) = (x^5)' => f'(x) = 5x^4`

Substituting 2 for x yields:

`f'(2) = 5*2^4 => f'(2) = 5*16 => f'(2) = 80`

Hence, evaluating the rate of change of the given function, at the point `(2,32),` yields `f'(2) = 80` .

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