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let f(x)=e^(-6x^2)
then f(x) has a relative minimum at x=__
a
inflection points at x=__
Thank you!
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- How do I solve the derivative for x to find the critical points and identify the absolute minimum and maximum?Suppose you find the linear approximation to a differentiablefunction at a local maximum of that function. Describe the graphof the linear approximation.Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local minimum at the critical point x = 0.
- Analyze the functions whose derivatives is given below. What are the critical points of ƒ? On what open intervals is ƒ increasing or decreasing? At what points, if any, does ƒ assume local maximum and minimum values?With the use of examples, differentiate between horizontal integration andvertical integration.Where do the minimum instantaneous rates of change occur for the function shown here?
- obtain general and particular solution satisfying initial condition indicated using homogenous functionHow do you find the critcial point and absolute minimum?The base of a rectangular box, open at the top, is to be three times as long as it is wide.Find the dimensions of the box with minimal surface area if the volume of the box is to be 2250 cubicinches. Show and organize your work; use the first derivative test or the second derivative test orother tools to check that yours is the desired optimal solution.
- Does this fuction have a minimum value?6. Use the first derivative to determine where the function is increasing and decreasing and where all relative maximums and minimums occur. Do not use the graphSketch the graph of a function with a critical point that is not an extremum and a critical point where the derivative does not exist but is an extremum.