Question

What is the equation of the tangent line of `f(x)=x^4 +2x^2` at `x=1`?

Answer 1

y = 8x - 5

Explanation:

To find the equation of the tangent we require it's gradient (m) and a point on it (a , b )

To find m we evaluate f'(x) and to find (a , b ) we evaluate f(1).

f ' (x) = `4x^3 + 4x`

`rArr f'(1) = 4 + 4 = 8 = m`

and f(1) = 1 + 2 = 3 so (1 , 3 ) is point on line.

equation of tangent : y - b = m (x - a ) , m = 8 , (a , b ) = (1 , 3 )

`rArr y - 3 = 8(x - 1 ) rArr y - 3 =8x - 8`

equation of tangent is : y = 8x - 5