Key to "What is the instantaneous rate of change of..."

Lisa Vaughan

Answered question

2022-03-14

What is the instantaneous rate of change of

f (x) = {(x - 5)}^{2}

at x=2?

jednakoga5u

Beginner2022-03-15Added 3 answers

Explanation:
Rate of change of

f (x) = {(x - 5)}^{2}

is given by

\frac{d f}{d x}

, which is given by

\frac{d f}{d x} = 2 \cdot (x - 5) = 2 x - 10

.
As at x=2,

\frac{d f}{d x} = 2 \times 2 - 10 = - 6

the instantaneous rate of change of f(x) at x=2 is -6.

sa1yap80

Beginner2022-03-16Added 2 answers

Solution:
The instantaneous rate of change of the function f(x) at the point

x = x_{0}

is the derivative of the function f(x) evaluated at the point

x = x_{0}

This means that we need to find the derivative of

{(x - 5)}^{2}

and evaluate it at x=2.
So, find the derivative of the function:

\frac{d}{d x} ({(x - 5)}^{2}) = 2 (x - 5)

Evaluate the derivative at x = 2.

(\frac{d}{d x} ({(x - 5)}^{2})) {|_{{(x = 2)}} = (2 (x - 5)) |}_{(x = 2)} = - 6

Therefore, the instantaneous rate of change of

f (x) = {(x - 5)}^{2}

at x=2 is -6.

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