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Solved in 2 steps with 2 images
- How are the absolute maximum and minimum similar to and different from the local extrema?the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function because the second derivative is ..........(positive/negative).Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local minimum at the critical point x = 0.
- Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does the graph of ƒ have a local maximum, local minimum, or point of inflection?Use the graph of the first derivative function f'(x) to find x values at which function has relative minimum and relative maximum.Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.
- Obtain the general and particular solution satisfying initial condition indicated using homogenous functionGive an example of a differentiable function ƒ whose first derivative is zero at some point c even though ƒ has neither a local maximum nor a local minimum at c.How do I solve the derivative for x to find the critical points and identify the absolute minimum and maximum?
- Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does the graph of ƒ have a local maxi-mum, local minimum, or point of inflection?For bubble 4, Please *CLEARLY* point out what the coordinate points are of the extreme and *CLEARLY* label each point as the minimum or maximum, using the second derivative test.Find the derivative of the function by the limit process. f(x) = x2 + x − 3