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Let f be the function defined by f(x) = 6 exp(x2 - 3x). The function exp(u) is another name for eu.
a. Find L(x) the linear approximation to f at 3.
b. Use the Linear Approximation for f(x) = 6 exp(x2 - 3x) at 3 to estimate f(3.06).
c. Find the error in the linear approximation to the value of f(3 + 0.06) that we found in part b).
d. Find the percentage that results from approximation f(3 + 0.06) by the value in part b).
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The manufacturer can produce the lamps at a cost of $4 per lamp. At what price should the manufacturer sell the lamp to generate the greatest possible profit?
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