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Popular >

h(t)=(t+1)^{2/3}(2t^2-1)^3

Solution

h (t) = (t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3}

Solution

Domain : - \infty < t < \infty

Range : f (t) \geq (\frac{97298 - 9477 \cdot 10 1 ^{\frac{1}{2}}}{125000} - 1) (\frac{- 9 + 10 1 ^{\frac{1}{2}}}{20} + 1)^{\frac{2}{3}}

X Intercepts : (- 1, 0), (- \frac{1}{2 ^{\frac{1}{2}}}, 0), (\frac{1}{2 ^{\frac{1}{2}}}, 0), Y Intercepts : (0, - 1)

Asymptotes : None

Extreme Points : Minimum (- 1, 0), Maximum - \frac{9 + 10 1 ^{\frac{1}{2}}}{20}, (\frac{97298 + 9477 \cdot 10 1 ^{\frac{1}{2}}}{125000} - 1) (- \frac{9 + 10 1 ^{\frac{1}{2}}}{20} + 1)^{\frac{2}{3}}, Saddle (- \frac{1}{2 ^{\frac{1}{2}}}, 0), Minimum \frac{- 9 + 10 1 ^{\frac{1}{2}}}{20}, (\frac{97298 - 9477 \cdot 10 1 ^{\frac{1}{2}}}{125000} - 1) (\frac{- 9 + 10 1 ^{\frac{1}{2}}}{20} + 1)^{\frac{2}{3}}, Saddle (\frac{1}{2 ^{\frac{1}{2}}}, 0)

+1

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

(t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3} : - \infty < t < \infty

Range of

(t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3} : f (t) \geq (\frac{97298 - 9477 \cdot 10 1 ^{\frac{1}{2}}}{125000} - 1) (\frac{- 9 + 10 1 ^{\frac{1}{2}}}{20} + 1)^{\frac{2}{3}}

Axis interception points of

(t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3} :

X Intercepts

: (- 1, 0), (- \frac{1}{2 ^{\frac{1}{2}}}, 0), (\frac{1}{2 ^{\frac{1}{2}}}, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

(t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3} :

None

Extreme Points of

(t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3} :

Minimum

(- 1, 0),

Maximum

- \frac{9 + 10 1 ^{\frac{1}{2}}}{20}, (\frac{97298 + 9477 \cdot 10 1 ^{\frac{1}{2}}}{125000} - 1) (- \frac{9 + 10 1 ^{\frac{1}{2}}}{20} + 1)^{\frac{2}{3}},

Saddle

(- \frac{1}{2 ^{\frac{1}{2}}}, 0),

Minimum

\frac{- 9 + 10 1 ^{\frac{1}{2}}}{20}, (\frac{97298 - 9477 \cdot 10 1 ^{\frac{1}{2}}}{125000} - 1) (\frac{- 9 + 10 1 ^{\frac{1}{2}}}{20} + 1)^{\frac{2}{3}},

Saddle

(\frac{1}{2 ^{\frac{1}{2}}}, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the h(t)=(t+1)^{2/3}(2t^2-1)^3 ?
The h(t)=(t+1)^{2/3}(2t^2-1)^3 is