Question

What is the equation of the line tangent to `f(x)=x^4 + 9x^2 − x` at `x=1`?

Answer 1

y = 21x - 12

Explanation:

Require to find f'(1) which is the value of the tangent gradient (m)

equation of tangent in form y = mx + c

Also require f(1) to find value of c .

hence f'(x) `= 4x^3 + 18x - 1`

and f'(1) = 4+18-1= 21 also f(1) = 1+9-1 = 9 → (1,9)

equation then is y = 21x + c and using ( 1,9) to find c .

hence : 9 = 21 + c → c = - 12

therefore equation of tangent is y = 21x - 12