Hi,
I have these two problems that I'm having trouble with
1.) 12x^3 - 14x^2 -28x + 16
I find the derivative --> f'(x) = 36x^2 - 28x - 28
then I use the Quadratic Formula and get x= 28 (plus/minus) the square root of 4816
OVER 72
Where do I go from here to simplify it?? I know it 28/72 can be reduced to 7/18, but how do I simplify the square root of 4816 over 72?? I got x= 7/18 (plusminus) 4 . (the sq. root of 1204) over 72
2.) 8x^3 + 30x^2 - 11x - 12
f'1(x)= 24x^2 + 60x - 11
I get x= -60 (plus/minus) the squareroot of 4656
all over 48
I don't know how to simplify this? PLEASE show steps and help!!
I have these two problems that I'm having trouble with
1.) 12x^3 - 14x^2 -28x + 16
I find the derivative --> f'(x) = 36x^2 - 28x - 28
then I use the Quadratic Formula and get x= 28 (plus/minus) the square root of 4816
OVER 72
Where do I go from here to simplify it?? I know it 28/72 can be reduced to 7/18, but how do I simplify the square root of 4816 over 72?? I got x= 7/18 (plusminus) 4 . (the sq. root of 1204) over 72
2.) 8x^3 + 30x^2 - 11x - 12
f'1(x)= 24x^2 + 60x - 11
I get x= -60 (plus/minus) the squareroot of 4656
all over 48
I don't know how to simplify this? PLEASE show steps and help!!
-
Hi,
Just as a reality check, my graphing calculator gives x=-0.574 for the max and x=1.35 for the min. So, let’s take a look at the derivative for the first one.
f’(x) = 36x^2 -28x-28
36x^2 -28x-28 =0
4(9x^2-7x-7)=0 (Factor out GCF of 4)
x=-b±√(b^2-4ac)/(2a)
=[-(-7) ±√((-7)^2-4(9)(-7)]/(2*9)
=[7±√(49+252)]/18
=[7±√(301)]/18
That’s about .3889±.9639
2) For this one the calc gives: max = -2.6715, min = 0.1716
f’(x) = 24x^2 +60x – 11
24x^2 +60x-11=0
x=[-60±√(60^2-4(24)(-11)]/(2*24)
=[-60±√(3600 +1056]/48
=-5/4 ±[√(16*291)]/48
=[-5/4±[4√(291)]/48]
I’ll leave it to you to check this with the calculator.
formeng
Just as a reality check, my graphing calculator gives x=-0.574 for the max and x=1.35 for the min. So, let’s take a look at the derivative for the first one.
f’(x) = 36x^2 -28x-28
36x^2 -28x-28 =0
4(9x^2-7x-7)=0 (Factor out GCF of 4)
x=-b±√(b^2-4ac)/(2a)
=[-(-7) ±√((-7)^2-4(9)(-7)]/(2*9)
=[7±√(49+252)]/18
=[7±√(301)]/18
That’s about .3889±.9639
2) For this one the calc gives: max = -2.6715, min = 0.1716
f’(x) = 24x^2 +60x – 11
24x^2 +60x-11=0
x=[-60±√(60^2-4(24)(-11)]/(2*24)
=[-60±√(3600 +1056]/48
=-5/4 ±[√(16*291)]/48
=[-5/4±[4√(291)]/48]
I’ll leave it to you to check this with the calculator.
formeng
-
Now x will be either [7+sqrt(301)]/18....a or [7-sqrt(301)]/18....b
for max double diff should be neg
if u diff. Again u will get 72x-28
now if x is as eq...a then double diff of given eq becomes positive hence minima and so eq....b is maxima.(substitute values of x in the double differentiated eq to find which one will be positive and vice versa)
for max double diff should be neg
if u diff. Again u will get 72x-28
now if x is as eq...a then double diff of given eq becomes positive hence minima and so eq....b is maxima.(substitute values of x in the double differentiated eq to find which one will be positive and vice versa)