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Popular >

y=3e^{2x}+e^{-2x}-3x

Solution

y = 3 e^{2 x} + e^{- 2 x} - 3 x

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq - 3 (\frac{1}{2} ln (3 + 57) - ln (2) - \frac{1}{2} ln (3)) + \frac{57}{2}

Y Intercepts : (0, 4)

Asymptotes : None

Extreme Points : Minimum (\frac{1}{2} ln (3 + 57) - (ln (2) + \frac{1}{2} ln (3)), - 3 (\frac{1}{2} ln (3 + 57) - ln (2) - \frac{1}{2} ln (3)) + \frac{57}{2})

+1

Solution steps

Domain of

3 e^{2 x} + e^{- 2 x} - 3 x : - \infty < x < \infty

Range of

3 e^{2 x} + e^{- 2 x} - 3 x : f (x) \geq - 3 (\frac{1}{2} ln (3 + 57) - ln (2) - \frac{1}{2} ln (3)) + \frac{57}{2}

Axis interception points of

3 e^{2 x} + e^{- 2 x} - 3 x :

Y Intercepts

: (0, 4)

Asymptotes of

3 e^{2 x} + e^{- 2 x} - 3 x :

None

Extreme Points of

3 e^{2 x} + e^{- 2 x} - 3 x :

Minimum

(\frac{1}{2} ln (3 + 57) - (ln (2) + \frac{1}{2} ln (3)), - 3 (\frac{1}{2} ln (3 + 57) - ln (2) - \frac{1}{2} ln (3)) + \frac{57}{2})

Popular Examples

y = x + \frac{1}{2 x}

f (x) = 8 x^{10}

f(x)=log_{10}(sin(x+3))

f (x) = lo g_{10} (sin (x + 3))

y=\sqrt[5]{x^3}

f (x) = 8 (\frac{3}{4})^{x}

Frequently Asked Questions (FAQ)

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