Question

What is the equation of the tangent line passing through the point (1, 3) of the graph of the function f(x) = x2 + x + 1?

Answer 1

Answer: y=3x

Step-by-step explanation: I got this right on Edmentum

Answer 2

`y = 3x`

Step-by-step explanation

The given function is

`f(x) = {x}^(2) + x + 1`

To find the gradient function, we find the first derivative;

`f'(x) = 2x+ 1`

To find the gradient at (1,3), we put x=1 into the gradient function to get;

`f'(1) = 2(1)+ 1 = 3`

The equation of the tangent line is

`y-y_1=m(x-x_1)`

We substitute the point and the slope to get,

`y-3=3(x-1)`

This simplifies to

`y = 3x - 3 + 3`

`y = 3x`