What is the range of x^3-x^4 ?

The range of x^3-x^4 is f(x)<= 27/256

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range of x^3-x^4

range

x^{3} - x^{4}

f (x) \leq \frac{27}{256}

Solution steps

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

Domain of

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

Extreme Points of

x^{3} - x^{4} :

Saddle

(0, 0),

Maximum

(\frac{3}{4}, \frac{27}{256})

Find the range for the interval

- \infty < x < \infty : - \infty < f (x) \leq \frac{27}{256}

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

f (x) \leq \frac{27}{256}

y = - 7 x - 51

f (x) = 4 x^{3} - 48 x - 3

6 x^{2} + 12 x

y = 1.1 x

y = \frac{x ^{2} + 3 x + 7}{2 x - 1}