What is the instantaneous rate of change of #f(x)=-2x^3+5 x^2+3x # at #x=-2#?

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Answer 1 · 2017-06-15T21:42:09

#x=-41#

What you want to do first is find the derivative using the power rule.
The derivative is the instantaneous rate of change.

Which states:

#d/dxx^n=nx^(n-1)#

#d/dx=-(3)2x^(3-1)+(2)5x^(2-1)+(1)3x^(1-1)#

Please keep in mind that #x^(1-1)=x^0=1#

#d/dx=-6x^2+10x+3#

Now you plug in #x=-2#

#-6(-2)^2+10(-2)+3=-41#