What is the equation of the tangent line

Jerimiah Boone

Jerimiah Boone

Answered question

2022-03-15

What is the equation of the tangent line of f(x)=x4+2x2 at x=1?

Answer & Explanation

varkdrafx9w

varkdrafx9w

Beginner2022-03-16Added 4 answers

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)=4x3+4x
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 )
y3=8(x1)y3=8x8
equation of tangent is : y = 8x - 5

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