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The derivative of a product of functions is equal to the derivative of the first function...
Question 8 4 pts At an inflection point for a function f, the second derivative is Oor does not exist. True O False
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
Use first derivative analysis (no calculators) to graph each function. (By first derivative analysis we mean the following as demonstrated in class: find critical values indicate whether the first derivative is 0 (producing a horizontal tangent) or undefined (producing sharp corner or vertical tangent) at each critical value o o o show tables of intervals where f increases or decreases and thus whether critical values correspond to a local maximum, local minimum, or neither). x) (4-x2) Use first derivative analysis...
3. (5 pts) For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter three, use the limit definition, Pay careful attention to the function names and independent variables. It is important to be comfortable with using letters other than f and r. For...
The directional derivative of the function f(x, y) = 2x In(y) in the direction v =< 0,1 > at the point (1,1) is equal to 2. Select one: O True False
-1 CSC х The derivative of the function y at a 1 is equal to I Select one: a. -1 b. Does not exist e c. O d. 1 The derivative of the function e5z - In z is equal to Select one: e5z-In 1 5 b.e х C. e5z-In z -5 d. e5z-Inz T
The derivative of the impulse function is the step function. True or False.
4. (a) A function f has first derivative f') and second derivative It is also known that the function f has r-intercept at (-3,0) and a y-intercept at (0,0) 0) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative. (ii) Use the f'(x), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points that are...
number 9 pleaseThe Following table gives a the signs of the first and second derivative of a function \(f(x)\) use this information to choose the correct Graph
Consider the following. 7 g(t) = 846 Find the first derivative of the function. g'(t) = Find the second derivative of the function. g"(t) = X Use the General Power Rule to find the derivative of the function. 1 y = 3 (8 - x3,8 y' = Find the derivative of the function. 3 8x 5 Y= 뉴 4-X y =