# How do you find the equation of a line tangent to the function #y=(x-2)(x^2+1)# at x=-1?

##### 2 Answers

#### Explanation:

Tangent Line to a Curve

simplify

differentiate

substitute for

the value of

and to get the point which lies on the tangent we substitute with

so the point on the line is

substitute in the following formula to get the equation

I hope this was helpful.

#### Explanation:

At

The tangent passes through

The gradient:

At

Since we have the gradient of the tangent and a point through which it passes we can use the point-gradient formula: