Question

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

Answer 1

Step-by-step explanation:

To find the derivative of

3x+5, apply sum rule

$\frac{d}{dx}(3x + 5) = \frac{d}{dx} 3x + \frac{d}{dx} 5$

The derivative of

$\frac{d}{dx} kx = k$

And

$\frac{d}{dx} c = 0$

So we have

$\frac{d}{dx} 3x + 5 = 3$

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.