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

2

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

Answer 2

4.5

Explanation:

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

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

Remember to use power rule:

`(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 + (2)/(4) = 4.5`