Question

1). Find the derivative of the function

f(x) = ln(x9 + 3) − 4ex/2 − x

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2). Find the equation for the tangent line to the curve y = f(x) at the given x-value.

f(x) = x ln(x − 5)  at  x = 6

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3). Use implicit differentiation to find dy/dx.

y² − ye^x = 19

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4). The United States population (in millions) is predicted to be P(t) = 317e^0.01t, where t is the number of years after 2013.† Find the instantaneous rate of change of the population in the year 2050. (Round your answer to two decimal places.)

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5). Election returns are broadcast in a town of 1 million people, and the number of people who have heard the news within t hours is 1,000,000(1 − e^−0.6t). How long will it take for 750,000 people to hear the news? (Round your answer to two decimal places.)

Answer 1