Question

Find the slope of the function when x=4

y=
2x+1/x2

Select one:
a. 386
b. 0.56 X
C. -0.16
d. 1/4
e. -0.125

Answer 1

Option C.

Explanation:

The given function is

`y=(2x+1)/(x^2)`

We need to find the slope of the function when x=4.

Differentiate the given function w.r.t. x.

`(dy)/(dx)=(x^2(d)/(dx)(2x+1)-(2x+1)(d)/(dx)x^2)/((x^2)^2)` (Using quotient rule)

`(dy)/(dx)=(x^2(2+0)-(2x+1)(2x))/(x^4)`

`(dy)/(dx)=(2x^2-4x^2-2x)/(x^4)`

`(dy)/(dx)=(-2x^2-2x)/(x^4)`

`(dy)/(dx)=(-2x(x+1))/(x^4)`

`(dy)/(dx)=(-2(x+1))/(x^3)`

Now substitute x=4 in the above equation.

`(dy)/(dx)_(x=4)=(-2(4+1))/(4^3)`

`(dy)/(dx)_(x=4)=(-2(5))/(64)`

`(dy)/(dx)_(x=4)=(-10)/(64)`

`(dy)/(dx)_(x=4)=-0.15625`

`(dy)/(dx)_(x=4)\approx -0.16`

Therefore, the correct option is C.