How do you find the instantaneous rate of change of y=x2−4x at x=1 by using the limit method?

Question

Ronnie Porter · Accepted Answer

Explanation:The instantaneous rate of change of y=f(x)=x2−4x at x=1 is the derivative f&#039;(1).Using the definition of the derivative in terms of limits, we have:f′(1)=limh→0f(1+h)−f(1)h=limh→0(1+h)2−4(1+h)−(1−4)h=limh→01+2h+h2−4−4h+3h=limh→0h(h−2)h=limh→0(h−2)=0−2=−2

obettyQuokeperg6 · Accepted Answer

This means that we need to find the derivative of

x^{2} - 4 x

and evaluate it at x=1.
So, find the derivative of the function:

\frac{d}{d x} (x^{2} - 4 x) = 2 (x - 2)

Evaluate the derivative at x=1.

(\frac{d}{d x} (x^{2} - 4 x)) {|_{{(x = 1)}} = (2 (x - 2)) |}_{(x = 1)} = - 2

Therefore, the instantaneous rate of change of

f (x) = x^{2} - 4 x

at x=1 is -2.

How do you find the instantaneous rate of change of

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