What is the range of f(x)=x^4+3x^3 ?

The range of f(x)=x^4+3x^3 is f(x)>=-2187/256

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range of f(x)=x^4+3x^3

range

f (x) = x^{4} + 3 x^{3}

f (x) \geq - \frac{2187}{256}

Interval Notation

[- \frac{2187}{256}, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

x^{4} + 3 x^{3} : - \infty < x < \infty

Extreme Points of

x^{4} + 3 x^{3} :

Minimum

(- \frac{9}{4}, - \frac{2187}{256}),

Saddle

(0, 0)

Find the range for the interval

- \infty < x < \infty : - \frac{2187}{256} \leq f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) \geq - \frac{2187}{256}

f (x) = \frac{2 ( x ^{2} - 1 )}{x ^{3}}

f (x) = 2^{5 - 8 x}

f (x) = \frac{1}{x - 10}

f (x) = - 9 x^{2} - 6 x - 1

f (x) = ln (x^{2} - 4 x + 5)

What is the range of f(x)=x^4+3x^3 ?
The range of f(x)=x^4+3x^3 is f(x)>=-2187/256