Find an equation of the tangent line to the graph of the function at the given point.

Question

Find an equation of the tangent line to the graph of the function at the given point

y=(e^4x-4)^2, (0,9)

y=_________

Answer 1

y = (e^4x - 4)²

y' = 2(e^4x - 4)(e^4x - 4)' = 2(e^4x - 4)(4e^4x)

At the point (0,9), y' = 2(-3)(4) = -24

Equation of tangent line at (0,9): y - 9 = -24(x - 0)

y = -24x + 9