Question

What is the instataneous rate of change at x=2 of the function f given by f(x)= x^2-2÷x-1​

Answer 1

Answer:

4.5

Step-by-step explanation:

To find the instantaneous rate of chance, take the derivative:

$f(x) = {x}^{2} - \frac{2}{x} - 1 \\ \frac{d}{dx} f(x) = 2x + \frac{2}{ {x}^{2} }$

Remember to use power rule:

$\frac{d}{dx} {x}^{a} = a {x}^{a - 1}$

To differentiate -2/x, think of it as:

$- 2 {x}^{ - 1}$

Then, substitute 2 for x:

$2(2) + \frac{2}{ {2}^{2} } \\ 4 + \frac{2}{4} = 4.5$

Answer 2

Answer:

2

Step-by-step explanation:

Assuming the function is:

f(x) = (x² − 2) / (x − 1)

Use quotient rule to find the derivative.

f'(x) = [ (x − 1) (2x) − (x² − 2) (1) ] / (x − 1)²

f'(x) = (2x² − 2x − x² + 2) / (x − 1)²

f'(x) = (x² − 2x + 2) / (x − 1)²

Evaluate at x=2.

f'(2) = (2² − 2(2) + 2) / (2 − 1)²

f'(2) = (4 − 4 + 2) / 1

f'(2) = 2