do you agree or disagree with the statement the marginal rate of change of the function f(x)=x^5 at the point (2,32) is 80? show working

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This is related to derivatives.


`y = x^5 ----(1)`


Let us say for for marginal change in `deltax` the change in y is `deltay `


`y+deltay = (x+deltax)^5 ----(2)`



`deltay = (x+deltax)^5-x^5`


Rate of change means `(deltay)/(deltax)`


`(deltay)/(deltax) = [(x+deltax)^5-x^5]/(deltax)`


When `(deltay)/(deltax)` be a small marginal change;


`lim_(xrarr0)(deltay)/(deltax) ` referred as the derivative of a function.

Therefore rate of marginal change can be expressed as the derivative.


Rate of change at x = 2 and y = 32;

`((dy)/dx)_(x=2) = 5*2^4 = 80`

So the statement is correct and we should agree with that.

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