Mathematics OpenStudy (anonymous):

I am having difficulty on Maxima and minima can some one explain me with an very easy eg as i am not good in my studies being frank OpenStudy (shadowfiend):

What particular issues are you having? Just understanding the concept in general? OpenStudy (anonymous):

$$I have understood the concept but getting the ans and what concept \it shows is really different 1(find the extreme values of f(x)=x^{3}-3x ^{2}-45x+25 got the solution Max=106 at x=-3 &Min value =-150 at x=5 Is \it \right ?$$ OpenStudy (shadowfiend):

So the problem is: $$f(x)=x^{3}-3x^{2}-45x+25$$ And you got: Maximum = 106 @ x = -3 Minimum = -150 @ x = 5 With a quick spot check, that looks right. You can spot check first by verifying that x = -3 and x = 5 are inflection points for that function. You can determine that by finding the derivative of $$f(x)$$ = $$f'(x)$$ using the basic power rule. $$\frac{d}{dx}x^3 - 3x^2 - 45x + 25 = f'(x) = 3x^2 - 6x - 45$$ You can plug in -3: $$3 \cdot -3^2 - 6 \cdot -3 - 45 = 27 + 18 - 45 = 0$$ And 5: $$3 \cdot 5^2 - 6 \cdot 5 - 45 = 75 - 30 - 45 = 0$$ Since the derivative is 0 at both, these two are inflection points. Once you determine that the values of $$f(x)$$ at x = -2 and x = -4 are lower than at x = -3, you know that x = -3 is the *maximum*. Once you determine that the values of $$f(x)$$ at x = 4 and x = 6 are higher than at = 5, you know that x = 5 is the *minimum*.

Latest Questions FrogGirlEmmy: can a unvaccinated Ferret play with a vaccinated ferret?
2 minutes ago 15 Replies 4 Medals Foreverangel: Complex changes have shaped Eurasia since the Soviet Union's disintegration in 1991.
40 minutes ago 3 Replies 0 Medals baileyadams: I suck at singing but anyway whats yalls opion ik its terrible https://voca.ro/14
1 hour ago 11 Replies 2 Medals omglolove12: What is something that charms you everytime you see it/them. for me its: youuuu!!
1 hour ago 1 Reply 0 Medals Joe348: Sinc everyone else was doing it.... how do i sound??? https://voca.ro/19FFNtqa4zR
1 hour ago 9 Replies 0 Medals aramondi: Calculate the number of grams of Fe2O3 needed to react with 19.0 g C.
20 minutes ago 1 Reply 0 Medals iosangel: Read the line from the first stanza of u201cO Captain! My Captain!u201d The ship
1 hour ago 3 Replies 0 Medals 5824234167: I hope you like this my voice cracked a little. Enjoy. Lovely Billie Eilish ft. K
1 hour ago 2 Replies 0 Medals brianagatica14: What do you think of my spawn drawing? I would like to hear any advice and answer honstely.
2 hours ago 7 Replies 4 Medals Rylee88: How do I write a fraction as a mixed number? ~Math
2 hours ago 3 Replies 1 Medal