# How do you find the equation of the tangent line to the curve #y=x^4+2x^2-x# at (1,2)?

##### 2 Answers

#### Explanation:

We have;

First we differentiate wrt

We now find the vale of the derivative at

So at the tangent passes through the coordinate

We now use

# :. y - 2 = 7 (x - 1) #

# :. y - 2 = 7x - 7 #

# :. y = 7x - 5 #

The equation of the tangent is

#### Explanation:

let

Then the derivative is

At the point

So the slope of the tangent is

The equation of the line is,

graph{(y-x^4-2x^2+x)(y-7x+5)=0 [-5.55, 5.55, -2.773, 2.776]}