What is the extreme f(x)=3x-5x^2,(-infinity <x<= 2) ?

The extreme f(x)=3x-5x^2,(-infinity <x<= 2) is Maximum(3/10 , 9/20),Minimum(2,-14)

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extreme f(x)=3x-5x^2,(-infinity <x<= 2)

extreme points

f (x) = 3 x - 5 x^{2}, (- \infty < x \leq 2)

Maximum (\frac{3}{10}, \frac{9}{20}), Minimum (2, - 14)

Solution steps

Find the critical points:

x = \frac{3}{10}, x = 2

Domain of

3 x - 5 x^{2}, - \infty < x \leq 2 : x \leq 2

Find intervals:

Increasing

: - \infty < x < \frac{3}{10},

Decreasing

: \frac{3}{10} < x < 2

Plug the extreme point

x = \frac{3}{10}

into

3 x - 5 x^{2} \Rightarrow y = \frac{9}{20}

Maximum (\frac{3}{10}, \frac{9}{20})

Plug the extreme point

x = 2

into

3 x - 5 x^{2} \Rightarrow y = - 14

Minimum (2, - 14)

Maximum (\frac{3}{10}, \frac{9}{20}), Minimum (2, - 14)

f (x) = 5 (10 - x) + 3 (16 + x^{2})

13 x^{2} - x^{3}

f (x) = 2 + 12 x - x^{2}

f (x) = (x - 3) (x + 1) (x + 4)

f (x) = x^{3} - 5 x^{2} + 7 x - 3

What is the extreme f(x)=3x-5x^2,(-infinity <x<= 2) ?
The extreme f(x)=3x-5x^2,(-infinity <x<= 2) is Maximum(3/10 , 9/20),Minimum(2,-14)