What is the range of (2-5x)sqrt(x) ?

The range of (2-5x)sqrt(x) is f(x)<= (4sqrt(2))/(3sqrt(15))

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range of (2-5x)sqrt(x)

range

(2 - 5 x) x

f (x) \leq \frac{4 2}{3 15}

Interval Notation

(- \infty, \frac{4 2}{3 15}]

Solution steps

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

Domain of

(2 - 5 x) x : x \geq 0

Extreme Points of

(2 - 5 x) x :

Minimum

(0, 0),

Maximum

(\frac{2}{15}, \frac{4 2}{3 15})

Find the range for the interval

0 \leq x < \infty : - \infty < f (x) \leq \frac{4 2}{3 15}

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

f (x) \leq \frac{4 2}{3 15}

f (x) = 3 cos (x)

y = - 3 x - 2

y = - 3 x + 5

f (x) = - 2 x + 1

What is the range of (2-5x)sqrt(x) ?
The range of (2-5x)sqrt(x) is f(x)<= (4sqrt(2))/(3sqrt(15))