Question

Derivative: find a slope of tangent line=square root of 4-5x when x=-1 ?

I want to know which formula will work to find slope in derivative and what will be its answer.

Answer 1

`m=(-5)/6`

Explanation:

For square roots, I like to change the notation to exponential notation rather than radical notation:

`sqrt(4-5x)=(4-5x)^(1/2)`

So now we have

`y=(4-5x)^(1/2)`

`(dy)/(dx)=1/2(4-5x)^(-1/2)*d/(dx)(4-5x)`

`(dy)/(dx)=1/2(4-5x)^(-1/2)*(-5)`

Change back to radical notation

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

Substituting x=-1 gives us

`m=(-5)/(2sqrt((4-5(-1))))=(-5)/(2sqrt(9))=(-5)/6`