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Popular >

f(x)=(x^2-6x+8)e^{x/2}

Solution

f (x) = (x^{2} - 6 x + 8) e^{\frac{x}{2}}

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq e^{\frac{1 + 5 ^{\frac{1}{2}}}{2}} (8 - 4 \cdot 5^{\frac{1}{2}})

X Intercepts : (4, 0), (2, 0), Y Intercepts : (0, 8)

Asymptotes : Horizontal y = 0

Extreme Points : Maximum (1 - 5^{\frac{1}{2}}, e^{\frac{1 - 5 ^{\frac{1}{2}}}{2}} (8 + 4 \cdot 5^{\frac{1}{2}})), Minimum (1 + 5^{\frac{1}{2}}, e^{\frac{1 + 5 ^{\frac{1}{2}}}{2}} (8 - 4 \cdot 5^{\frac{1}{2}}))

+1

Solution steps

Domain of

(x^{2} - 6 x + 8) e^{\frac{x}{2}} : - \infty < x < \infty

Range of

(x^{2} - 6 x + 8) e^{\frac{x}{2}} : f (x) \geq e^{\frac{1 + 5 ^{\frac{1}{2}}}{2}} (8 - 4 \cdot 5^{\frac{1}{2}})

Axis interception points of

(x^{2} - 6 x + 8) e^{\frac{x}{2}} :

X Intercepts

: (4, 0), (2, 0),

Y Intercepts

: (0, 8)

Asymptotes of

(x^{2} - 6 x + 8) e^{\frac{x}{2}} :

Horizontal

: y = 0

Extreme Points of

(x^{2} - 6 x + 8) e^{\frac{x}{2}} :

Maximum

(1 - 5^{\frac{1}{2}}, e^{\frac{1 - 5 ^{\frac{1}{2}}}{2}} (8 + 4 \cdot 5^{\frac{1}{2}})),

Minimum

(1 + 5^{\frac{1}{2}}, e^{\frac{1 + 5 ^{\frac{1}{2}}}{2}} (8 - 4 \cdot 5^{\frac{1}{2}}))

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Frequently Asked Questions (FAQ)

What is the f(x)=(x^2-6x+8)e^{x/2} ?
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