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

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Answer 1 · 2017-07-04T21:21:41

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

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

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