Question

Найди наибольшее значение линейной функции y=6x+2 на отрезке [0;2], не выполняя построения.

Answer 1

1 способ (без применения производной):
у=6х+2   [0;2]
у=6х+2 - возрастающая линейная функция, т.к. k=6>0
Следовательно, наибольшее значение данная функция принимает в правой части отрезка [0;2]
у(наиб.)=у(2)=6*2+2=12+2=14
Ответ: у(наиб.)=14

2 способ ( с применением производной):
y`(x)=(6x+2)`=6
6∉[0;2]
y(0)=6*0+2=2- наименьшее на [0;2]
y(2)=6*2+2=12+2=14 - наибольшее на [0;2]
Ответ: у(наиб.)=14

Answer 2

У=0 6х+2=0
6х=-2
х=-2/6= -1/3
наибольшее значение 0

Answer 3

Finding the Maximum Value of a Linear Function

To find the maximum value of the linear function y = 6x + 2 on the interval [0, 2], we can use the fact that the maximum or minimum value of a linear function occurs at the endpoints of the interval or at the critical points.

In this case, the interval [0, 2] has endpoints at x = 0 and x = 2. We can evaluate the function at these points to determine the maximum value.

1. Evaluating the function at x = 0: - y = 6(0) + 2 = 2

2. Evaluating the function at x = 2: - y = 6(2) + 2 = 14

Comparing the values, we can see that the maximum value of the linear function y = 6x + 2 on the interval [0, 2] is y = 14.

Please note that the maximum value of a linear function occurs at one of the endpoints of the interval when the slope is positive, as is the case here with a slope of 6. If the slope were negative, the minimum value would occur at one of the endpoints.

I hope this helps! Let me know if you have any further questions.