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strojnjashka [21]
3 years ago
15

Please please help thank you

Mathematics
1 answer:
Tcecarenko [31]3 years ago
7 0

Answer:

b-4^3

Step-by-step explanation:

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Help me please???<br> I don’t know how to get started!
Sliva [168]

A differentiable function f(x) is increasing on an open interval (a,b) if f'(x)>0 for all a, and decreasing if f'(x). For this problem, you then need to compute the derivative:

f(x)=x^2\ln x\implies f'(x)=2x\ln x+x=(2\ln x+1)x

then solve for f'(x)=0:

(2\ln x+1)x=0\implies x=0\text{ or }x=e^{-1/2}

We can ignore x=0 because x^2\ln x is defined only for x>0. So we have two intervals to consider, (0,e^{-1/2}) and (e^{-1/2},\infty). All we need to do is pick any value from either interval and check the sign of the derivative f'(x). Since e^{-1/2}\approx0.606, from the first interval we can take x=\dfrac12, and from the second we can pick x=1.

f'\left(\dfrac12\right)\approx-0.193

f'(1)=1>0

The above indicates that f(x) is decreasing on the first interval (0,e^{-1/2}), and increasing on the second interval (e^{-1/2},\infty).

For part (b), we use the info from above as part of the first derivative test for extrema. We have one critical point at x=e^{-1/2}, and we know how f(x) behaves to either side of this point; f(x) decreases to left of it, and increases to the right. This pattern is indicative of a minimum occurring at x=e^{-1/2}, and we find that f(x) has the (local) minimum value of f(e^{-1/2})=-\dfrac1{2e}\approx-0.184.

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3 years ago
Somebody please help me
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creativ13 [48]
3/6 and 1/2. 3/6 is 0.5 and 1/2 is 0.5, 0.5 x 0.5 = 0.25, and 1/4 = 0.25 so it is probably 1/4. Hope it helped if it didn't please let me know and i will corrected my self.
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