The derivative can exist at which of the following type of points? A) Sharp poin

Question

The derivative can exist at which of the following type of points? A) Sharp points B) Vertical tangent lines C) Relative extrema D) Non-removable discontinuities Which best defines the definition of a critical point x = c? A) Where f' (c) is undefined. B) Where f' (c) equals zero. C) Where f' (c) is undefined and where f' (c) equals zero D) Where f' (c) is undefined or where f' (c) equals zero and f (c) exists. A critical number of the function f (x) = x^2 ln (Squareroot x) on the interval (0, 2) is: A) (e^-1/2, 1/4 e) B) (e^1/2, -1/4e) C. (e^-1/2, -1/4e) D) (Squareroot e, 4/e) Find the equation of the tangent line at the point x = 1 for the function f (x) = In (x) + e^. A) y - e = (x + 1) B) y = -ex + x + 1 C) y = ex + x - 1 D) y' - e + 1 Let y = 3x - 5/x - 4 find dy/dx. A) -7/(x - 4)^2 B) -7 (x - 4)^2 C) -7/Squareroot x - 4 D) 3/1 Let: y = ln |x^2 + 2x| find D y. A) x + 2x/x^2 + 2x B) 2x + 2/x^2 + 2x C) x^2 + 2x/2x + 2) D) |2x + x/x^2 + 2x| Find D, y for y = 2^log_2 (x). A) ln (2) 2^log_2 (x) B) 2^(1/ln (2) x + ln (2) log_2 (x)) C) 2^/ln (2) x + log_2 (x) D) 1/ln (2) x + ln (2) log_2 (x) The best method for finding absolute extrema is: A) The 1st derivative test B The 2nd derivative test c) Find f (x) at critical and end points D) Evaluate f (x) at the end points s which statement best describes the (Briggs calculus) 2^nd Fundamental Theorem of Calculates? A) integral^b _a f (x) dx F (b) - F (a) B) integral^a _b F (x) dx = f (b) - f (a) C) integral^b _a F (x) dx = f (x) + c D) integral f (x) dt = F (x) + c

Explanation / Answer

Question 1 : option D

Question 2 : option B

Question 3: option c

Question 4 : option c

Question 5 : option A

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