作业帮Find the inflection points,if any,of the following function.Otherwise,answer no solution?f(x) = x^4 - 2x^3 +5 f(x) = 2/(1+x^2)
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Find the inflection points,if any,of the following function.Otherwise,answer no solution?f(x) = x^4 - 2x^3 +5 f(x) = 2/(1+x^2)
Find the inflection points,if any,of the following function.Otherwise,answer no solution?
f(x) = x^4 - 2x^3 +5
f(x) = 2/(1+x^2)
Find the inflection points,if any,of the following function.Otherwise,answer no solution?f(x) = x^4 - 2x^3 +5 f(x) = 2/(1+x^2)
f'(x) = 4x³ - 6x²
f"(x) = 12x² - 12x = 12x(x - 1) = 0
x = 0 or x = 1
x < 0,f"(x) > 0
0 < x < 1,f"(x) < 0
f(0) = 5,(0,5) is one inflection point
x > 1,f"(x) > 0
f(1) = 4,(1,4) is the other inflection point
f(x) = 2/(1 + x²),f'(x) = -4x(1 + x²)²
f"(x) = 4(3x² - 1)/(1 + x²)³ = 0
x = ±1/√3
x < -1/√3,f"(x) > 0
-1/√3 < x < 1/√3,f"(x) < 0
f(-1/√3) = 3/2,(-1/√3,3/2) is one inflection point
x > 1/√3,f"(x) > 0
f(1/√3) = 3/2,(1/√3,3/2) is the other inflection point