Question

What is the derivative and the slop of the tangent line of f(x)=3x+5 at (1,8)

Answer 1

Explanation:

To find the derivative of

3x+5, apply sum rule

`(d)/(dx)(3x + 5) = (d)/(dx) 3x + (d)/(dx) 5`

The derivative of

`(d)/(dx) kx = k`

And

`(d)/(dx) c = 0`

So we have

`(d)/(dx) 3x + 5 = 3`

So the derivative of the function is 3,

Since linear equations have a constant slope, the slope at any point will be 3.

So the slope of the tangent line is 3.