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

$y = 3x$

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

$y = 3x - 3 + 3$

$y = 3x$