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Straighterline MAT 250 Graded Exam 2

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Given , ¦nd by implicit differentiation. Select one: a. b. c. d. 5x2 + 2y3 = 10 dy dx 5 3 x 2y − 5 3 x 2y x 2y 3−5 x 2y9/5/2021 Graded Exam 2 https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095482 2/11 Question 2 Correct 5.00 points out of 5.00 Question 3 Correct 5.00 points out of 5.00 Question 4 Correct 5.00 points out of 5.00 Compute the derivative of the function . Select one: a. b. c. d. What is the derivative of the function ? Select one: a. b. c. d. $ 3x^2+2e^x $ What is the derivative of the function $ f(x)= \sqrt{x} $? Select one: a. $ \displaystyle \frac{1}{\sqrt{x}} $ b. $ \displaystyle \frac{1}{2\sqrt{x}} $ c. $ \displaystyle \frac{2}{\sqrt{x}} $ d. $ \displaystyle \frac{1}{2} $ f(x) = sec x cos x − tan x sec x sin2 x tan x sec x f(x) = x3 + 2e2x 3x2 + 4e2x 3x2 + 2e2x 3x2 + 2e29/5/2021 Graded Exam 2 https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095482 3/11 Question 5 Incorrect 0.00 points out of 5.00 Question 6 Correct 5.00 points out of 5.00 Evaluate the following as true or false. If $ f(x) = x^N $, where N is some number, then $ f'(x) = Nx $. Select one: a. true b. false The width $ x $ of a rectangle is decreasing at $ 3\, \hbox{cm/s} $, and its length $ y $ is increasing at $ 5\, \hbox{cm/s} $. At what rate is its area $ A $ changing when $ x = 10\, \hbox{ cm} $ and $ y = 15\, \hbox{ cm} $? Select one: a. $ 1/5\, \hbox{cm}^2\hbox{/s} $ b. $ -5\, \hbox{cm}^2\hbox{/s} $ c. $ 5\, \hbox{cm}^2\hbox{/s} $ d. none of the above9/5/2021 Graded Exam 2 https://moodle.straighterline.com/mod/quiz/review.php?attempt=4095482 4/11 Question 7 Correct 5.00 points out of 5.00 Question 8 Correct 5.00 points out of 5.00 Compute the derivative of the function $ f(x) = (-3x^4+5x^2-\sqrt{x}+3)\,(x^{-2}-6x) $. Select one: a. $ \bigg( -12\,x^3+10x+ \displaystyle \frac{1}{2}x^{-\frac{1}{2}} \bigg) (x^{-2}-6x)\\ \quad\quad\quad\quad\quad +(-3x^4+5x^2-\sqrt{x}+3)\, (-2x^{-3}-6) $ b. $ \bigg( -12\,x^3+10x- \displaystyle \frac{1}{2}x^{-\frac{1}{2}} \bigg) \, (x^{-2}-6x)\\ \quad\quad\quad\quad\quad+(-3x^4+5x^2-\sqrt{x}+3)\, (-2x^{-3}-6) $ c. $ \bigg( -12\,x^3+10x- \displaystyle \frac{1}{2}x^{-\frac{3}{2}} \bigg) (x^{-2}-6x)\\ \quad\quad\quad\quad\quad +(-3x^4+5x^2-\sqrt{x}+3)\, (-2x^{-3}-6) $ d. $ \bigg( -12\,x^3+10x- \displaystyle \frac{1}{2}x^{-\frac{3}{2}} \bigg) (-2x^{-3}-6) $ Find all points on $ xy=e^{xy} $ where the tangent line is horizontal. Select one:

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