If you're asking for extrema, like the previous posting
well
![\bf f(x)=\cfrac{-x}{x^2+5} \\\\\\ \cfrac{df}{dx}=\cfrac{(x^2+5)+2x^2}{(x^2+5)^2}\implies \cfrac{df}{dx}=\cfrac{5+3x^2}{(x^2+5)^2}\impliedby \begin{array}{llll} using\ the\\ quotient\ rule \end{array}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%5Ccfrac%7B-x%7D%7Bx%5E2%2B5%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdf%7D%7Bdx%7D%3D%5Ccfrac%7B%28x%5E2%2B5%29%2B2x%5E2%7D%7B%28x%5E2%2B5%29%5E2%7D%5Cimplies%20%5Ccfrac%7Bdf%7D%7Bdx%7D%3D%5Ccfrac%7B5%2B3x%5E2%7D%7B%28x%5E2%2B5%29%5E2%7D%5Cimpliedby%20%0A%5Cbegin%7Barray%7D%7Bllll%7D%0Ausing%5C%20the%5C%5C%0Aquotient%5C%20rule%0A%5Cend%7Barray%7D)
like the previous posting, since this rational is identical, just that the denominator is negative, the denominator yields no critical points
and the numerator, yields no critical points either, so the only check you can do is for the endpoints, of 0 and 4
f(0) = 0 <---- only maximum, and thus absolute maximum
f(4) ≈ - 0.19 <---- only minimum, and thus absolute minimum
Answer:
4z -6< - 10= Z= < -1
5z - 3 >7= Z=< 2
Step-by-step explanation:
-- After dog ate 1/2 of the collection, there were 29 remaining.
-- Just before dog came along, there were (2 x 29) = 58 cards.
-- That was after Dan added 5 new ones.
-- Before he added the 5 new ones, there were (58 - 5) = 53 cards.
-- When this story began, Dan had <em>53 cards</em>.
Answer:
12
Step-by-step explanation:
The least common multiple of {6,8,12} is 24. This can be intuitively figured by noting that any multiple of 12 is a multiple of 6 and that 12 is 1.5x larger than 8. That means we only have so multiple 12 by 2 and 8 by 3 for them to be equal. The GCF of {20,42,72} is 2 as the prime factorization of 20 is 2x2x5 and 42 is 2x3x7. That means even without having to check 72 (which is clearly even so 2 is a factor), we know that 2 is the greatest common factor that they could share. So X/Y = 24/2 = 12
? ?? Hi so that doesn’t make sense