The first derivative of a cont ys f(X) is y' = x(x-6r Find y" and then use the graphing procedure...
(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...
4. (a) A function f has first derivative f'(x) and second derivative 2 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. 3 marks] (ii) Use the f(x), and the First Derivative Test to classify each critical point.[3 marks] (iii) Use the second derivative to examine the...
4. (a) A function f has first derivative f' (x) - and second derivative 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. 3 marks] (ii) Use the f'(x), and the First Derivative Test to classify each critical point. 3 marks (iii) Use the second derivative to examine...
)and second derivative 4. (a) A function f has first derivative f'(x) f(E) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0, Q) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative [3 marks] (ii) Use the f(x), and the First Derivative Test to classify each critical point.[3 marks] (ii) Use the second derivative to examine the concavity...
4. (a) A function f has first derivative f (r) - and second derivative f"(z) 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'(x), and the First Derivative Test to classify each critical point. (iii) Use the second derivative to examine the concavity around critical...
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4. (a) A function f has first derivative f' (a) and second derivative a2 (x +3) 3 It is also known that the function f has r-intercept at (-3,0), f"(z) and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine 3 marks (ii) Use the f'(x), and the First Derivative Test to classify each critical point. [3 marks (iii) Use the second derivative to...
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...
The graphing calculator window shows the graph of a function f(x) and its derivative function f(x). Decide which is the graph of the function and which is the graph of the derivative. Which of the following methods would be helpful in distinguishing the graph of the function from the graph of its derivative? O A. Compare the x-intercepts of each line to see if a horizontal tangent line occurs at that x-value on the other line. Y2 O B. Calculate...
Curve Sketching: Use the following guidelines to sketch the graph of y-f(x) x-5x (20 points) a. What are the behaviors of y when x->oo, or x--0? (3 points) b. What is the first derivative of this function? What are increasing intervals and decreasing intervals and max points and mini points? (6 points) c. What are the second derivative of this function? What are intervals for concavity upwards and concavity downwards and inflection points? (6 points) Use the above information (a,...
Use the numerical derivative feature of a graphing calculator to find the derivative of each function at the given x-value. (Round your answer to three decimal places.) f(x) = 37*+2 at x = -1 x + 3