Question

What is the equation of the tangent line of `f(x) =(x-3)(3x-e^(x^2))` at `x=3`?

Answer 1

`y=(9-e^9)x-3(9-e^9)`

Explanation:

I used the product rule to differentiate f(x):
`(x-3)(3-2xe^(x^2)) + (1)(3x-e^(x^2))`

When x=3, f'(x) = (9-e^9)
at x = 3, y = 0 (substituting 3 into original equation)

For the equation,
y-0 = f'(x)(x-3)

which gave me the answer above