Math / Calculus

QuestionProblem 3. Given a function $f(x)=e^{-x^{2}+4 x}$ (a) (6 points) find the minimum and maximum values attained by $f$ over an interval $[0,3]$ , (b) (2 points) find the equation of the tangent line to the graph of $f$ at a point $(0, f(0))$ .

Studdy Solution
(a) The maximum value of $f(x)$ on the interval $[0, 3]$ is $e^4$ at $x = 2$ , and the minimum value is $1$ at $x = 0$ . (b) The equation of the tangent line at $x = 0$ is $y = 4x + 1$ .

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