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: [Show More]

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