Question

FIVE STARS AND BRAINLIEST TO CORRECT ANSWER

Find the derivative of f(x) = 4 divided by x at x = 2.

Answer choices:
A) -4
B) -1
C) 1
D) 4

Answer 1

Given, f(x) = 4/x

We have to find the derivative of it.

First we have to use property of negative exponents. We know that, 1/a = a⁻¹.

So here, f(x) = 4/x = 4x⁻¹

f'(x) = 4×(-1)×(x)⁽⁻¹⁻¹⁾

= 4×(-1)×(x)⁻²

= (-4)(x)⁻²

= -4/x²

So we have got derivative of f(x) which is f'(x) = -4/x²

Now we have to find the derivative at x = 2. To find the value at x =2, we have to plug in 2 in the place of x.

f'(2) = -4/(2)² = -4/4 = -1

We have got the required answer derivative of f(x) at x =2 is -1

So option B is correct.