Qual é a equação da reta tangente de #f (x) = x ^ 4 + 2x ^ 2 # em # x = 1 #?

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