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Finding Absolute Extrema :Now it's time to see our first major application of derivatives. Specified a continuous function, f(x), on an interval [a,b] we desire to find out the absolute extrema of the function. To do this we will requierd many of the ideas which we looked at in the previous section.
Firstly, as we have an interval and we are considering that the function is continuous the Extreme Value Theorem described that we can actually do this. it is a good thing of course. We don't desire to be trying to determine something that may not exist.
Next, we illustrated in the earlier section that absolute extrema can take place at endpoints or at relative extrema. Also, from Fermat's Theorem we know that the list of critical points is also a list of all probable relative extrema. Thus the endpoints along with the list of all critical points will actually be a list of all probable absolute extrema.
Now we just required to recall that the absolute extrema are nothing more than the largest & smallest values which a function will take thus all that we actually required to do is get a list of possible absolute extrema, plug these points into our function and then recognize the largest & smallest values.
Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?
for all real numbers x, x 0
Mark is preparing a walkway around his inground pool. The pool is 20 by 40 ft and the walkway is intended to be 4 ft wide. Determine the area of the walkway? a. 224 ft 2 b.
economic order quantities (EOQ) Statistics may be utilized in ordering or making economic order quantities as EOQ. It is significant for a business manager to understand that
how to describe the locus of the equation x^2+6xy+y^2+z^2=1 in cylindrical polar coordinates?
A number of the form x + iy, where x and y are real and natural numbers and is called as a complex number. It is normally given by z. i.e. z = x + iy, x is called as the real part
If 3200 sweets cost 30 US Dollars how much will 13,500 sweets cost ?
-10b2*-5b2=
Do you subtract when you add integers.
Errors Are Useful : While teaching children, you must have found theft making mistakes off and on. How do you respond to the errors'? What do they tell you about the child-failur
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