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anonymous
 one year ago
Some help would be lovely !!:D
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is
g′(x)=(x^2–16)/(x−2)
, with x ≠ 2.
A)On what intervals is the graph of g concave down? Justify your answer
B)Write an equation for the tangent line to the graph of g at the point where x = 3.
anonymous
 one year ago
Some help would be lovely !!:D Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2) , with x ≠ 2. A)On what intervals is the graph of g concave down? Justify your answer B)Write an equation for the tangent line to the graph of g at the point where x = 3.

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2are you able to find g '' (x) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i got \[(x^2 4x + 16)/((x2)^2)\]

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438285855095:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep yep did that got plus or minus 4 for g'(x)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2If you complete the square for the numerator, you get this x^2  4x + 16 x^2  4x + 4  4 + 16 (x^2  4x + 4) + 12 (x2)^2 + 12 So this means that x^2  4x + 16 is always positive. The same applies to (x2)^2. Overall, g '' (x) is always positive

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2since g '' (x) is never negative, it's impossible for g to be concave down

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so if g''(x) is positive then g(x) is concave up?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2yeah g is concave up over all of g's domain

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay and as far as i can get on part b is getting the slope ... wich is 7

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now i need a point on the tangent line right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2g(3) = 4 which means (3,4) lies on the g(x) function use m = 7 x = 3 y = 4 with y = mx+b and solve for b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.04 = 7(3) + b 25 = b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay great thank you very much !!!

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.2glad to be of help

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438286497814:dw
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