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anonymous
 one year ago
(a) Find the critical numbers of the function f(x) = x^8(x − 3)^7. I dont have examples like this problem so Im having a bit of trouble, please help!
anonymous
 one year ago
(a) Find the critical numbers of the function f(x) = x^8(x − 3)^7. I dont have examples like this problem so Im having a bit of trouble, please help!

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idku
 one year ago
Best ResponseYou've already chosen the best response.1is there an interval on which you are to find critical numbers, or there is no interval given >

idku
 one year ago
Best ResponseYou've already chosen the best response.1anyway, I will tell you what to do, before you get to answer me.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the interval is not given

idku
 one year ago
Best ResponseYou've already chosen the best response.1So, you have to: 1) Differentiate the function (take the derivative of the f(x) ). 2) Set f`(x)=0, and the x values that are solutions to this are critical numbers. 3) Critical numbers are also values where f`(x) is undefined  IFF f(x) is defined on that value(s)  but if f(x) is undefined at this value(s) then it is NOT a critical number.

idku
 one year ago
Best ResponseYou've already chosen the best response.1Also, if you were given the interval [a,b] (specifically a closed interval) then a and b would automatically be (also) your critical numbers.

idku
 one year ago
Best ResponseYou've already chosen the best response.1Is the outline/plan clear ?

idku
 one year ago
Best ResponseYou've already chosen the best response.1ok, can you find f`(x) for me pliz ?

idku
 one year ago
Best ResponseYou've already chosen the best response.1you can use product rule (or logarithmic differentiation)

idku
 one year ago
Best ResponseYou've already chosen the best response.1Product d/dx [ f × g] = f` g + g` h

idku
 one year ago
Best ResponseYou've already chosen the best response.1i will post the provwe for product rule now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i have 8x^7 (x2)^7 what do i do now?

idku
 one year ago
Best ResponseYou've already chosen the best response.1y = f * g (where f and g are some functions of x) use logarithmic diff. ln(y) = ln(f * g) ln(y) = ln(f) + ln(g) now, f and g are big function, so for any function H, there is a chain rule such that: d/dx [ ln( H(x) ) ] = ( 1 / H(x) ) * H`(x) So here we will use chain for f and g differentiating: (dy/dx) * y=f`/f + g`/g dy/dx = (f`/f + g`/g) * y then look at what y is from the beginning of the problem and substitute. find common denom, and cancel things out

idku
 one year ago
Best ResponseYou've already chosen the best response.1No, that is not correct. don't think so

idku
 one year ago
Best ResponseYou've already chosen the best response.1f(x) = x^8(x − 3)^7 f`(x) = (x^8)` * (x − 3)^7 + x^8 * ( (x3)^7 )`

idku
 one year ago
Best ResponseYou've already chosen the best response.1f`(x) = 8x^7 * (x3)^7 + x^8 * 7(x3)^6

idku
 one year ago
Best ResponseYou've already chosen the best response.1anyway, u got f`(x) then find x values for f`(x)=0 f`(x)=undefined i got to go

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got x=0,3 and 24/15

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(b) What does the Second Derivative Test tell you about the behavior of f at these critical numbers? At x=? the function has a local max, a local min or neither?
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