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Find the derivative of the following function. f(x) = (2x - 3)(3x4 +7x) f'(x) = 2(3x4 + 7x)+(2x - 3)(12x3 +7) f'(x) = 2 + (12x3 + 7) f'(x) = 2(12x3 + 7) f'(x) = 2(3x4 +7x) – (2x - 3)(12x3 + 7)
Find the derivative of f(x) = 3x4 - 8x2+2x–7.
The derivative of the function f(0) = 96x + 12x2 – 20x3 + 3x4 has three roots:-1, 2, and 4. That is, f'(-1) = f'(2) = f'(4) = 0 and there are no other points where f'(x) = 0. Find the maximum and the minimum value of f on the interval (0,3). Explain how you arrive at your answer.
USING THE SECOND DERIVATIVE CRITERIA FIND THE CRITICAL POINTS OF F (X) AND DETERMINE IF THEY ARE LOCAL MAXIMUM OR MINIMUM 3x4 – 8x3 + 6x2
Find the derivative of the function. y= 3x4 +7 x2
5. Suppose that we have f(x)e. Use derivatives to answer the following questions. Solutions based on graphical or numerical work will receive no credit. (a) (4pts) Find f"(), the second derivative of f(x) (b) (2 pts) Confirm that x =-1 is a critical point of f(x). (Evaluate f'(-1), and make a conclusion. (c) (4pts) Use the second derivative test to classify -1 as a local max. or a local min. If the second derivative test is inconclusive, then say so....
Find the second derivative of the function. y = 4(x2 + 2x)3 y" = _______ Find the third derivative of the function. f(x) = x4-4x3 f'''(x) = _______
(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...
Apply the second derivative test to find the relative extrema of the function f(x)=ln(x2+x+1)
1. (20 points) The second derivative of a function f(x) satisfies f "(x) = 10x4 - 2 Moreover, f'(0) = 0 and f(1) = 0. (a) Find the function f(x). (b) Draw a graph of f(x). Indicate all asymptotes (if any), local maxima and minima, inflection points, intervals where f(x) is increasing, and intervals where f(x) is concave upward.