What is the tangent line to f(x) = (x^2 + x – 3)^4 at (1,1)?

Answer 1

In words first find the derivative of f(x), plug in x = 1 to get the slope and then use that slope to find the equation of the tangent line.

Derivative of f (x) is 4 (x ^2 + x - 3 ) ^3 (2x + 1)

Plug in x = 1 to get slope m = - 12

To get equation of tangent line set slope of - 12 = ( y - 1) / ( x - 1)

Rearrange to get y = - 12x + 13

Answer 2

f(x) = (x^2 + x – 3)^4

To find the tangent line, we need the slope and one point. Get the slope from f'(x)

f'(x) = 4*(x^2 + x – 3)^3 * (2x + 1)

evaluate this at x=1 to get the slope m.

Use the standard form y = mx + b. To find b, plug in the values for the given point (1,1) and solve for b:

1 = m*1 + b

b = 1 - m