Inactive Tutor answered • 03/09/14
Tutor
New to Wyzant
See answer provided by Richard P, as modified with my comment ... yes, the answer (minimum slope) is -2.
Sun K.
asked • 03/09/14Find the minimum value?
Find the minimum value of the slope of the curve y=x^5+x^3-2x.
Answer: -2
Please show all your work.
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2 Answers By Expert Tutors
Inactive Tutor answered • 03/09/14
Tutor
New to Wyzant
The slope is the derivative of the function.
f' = 5 x4 + 3 x2 -2
This factors as ( 5 x2 -2 ) ( x2 +1)
The minimum is obtained by setting the first factor to zero. So x2 = 2/5 and
x = ± sqrt(2/5)
Inactive Tutor
You calculated the SLOPE. To calculate the maximum of the slope, you need the second derivative of the original function, f''= 20x3+6x = 0. The realroot are x=0; there are two imaginary roots, + or - sqrt (-6/20).
THe only "real" solution is x = 0; when x = 0, the (maximum) slope is 5*0+3*0-2= -2, as given by Sun, in asking the question. Do you agree?
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03/09/14
Inactive Tutor
My mistake ... should have said "minimum" (slope), not "maximum."
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03/09/14
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Sun K.
03/09/14