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

Answer 1

Christopher Agresta

y = 21x - 12

need to determine f'(1), the tangent gradient's value (m).

tangent equation in the form y = mx + c

The value of c can also be found by using f(1).

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

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

y = 21x + c is the equation thus found, and c can be found using (1,9).

Consequently, 9 = 21 + c → c = -12

Consequently, the tangent equation is y = 21x - 12.

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Answer 2

Emilia Aguilar

The equation of the line tangent to f(x)=x^4 + 9x^2 − x at x=1 is y = 19x - 11.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.