Step-by-step explanation: In order to find the maximum value of a function, you can take the derivative of the function and equalize the result to 0.

f'(x)=(-3x^2 + 12x)'=-6x+12=0

x=2

When x is 2, the function will reach its maximum value.

f(2)=-3(2)^2 + 12.2 = -12 + 24 = 12

The maximum value (f(x)) is equal to 12 and the time passed is 2 minutes which is equal to 120 seconds.

6 0

3 years ago

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An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram.What is the area, in sq

tatyana61 [14]

<h2>Explanation:</h2><h2 />

The complete question is shown in the figure below. As you can see one square units is well shown in the graph. So we can conclude that the distance between two consecutive points is 1 unit. If so, then we can calculate the area of the parallelogram as follows:

$A=b\times h \\ \\ A:Area \\ \\ b:Base \\ \\ h:Height \\ \\ \\ CB=b \\ \\ AB=h$

Then, finding CB by Pythagorean Theorem:

$CB=\sqrt{6^2+4^2} \\ \\ CB=2\sqrt{13}$

And:

$AB=4$

Therefore:

$A=(2\sqrt{13})(4) \\ \\ \boxed{A=8\sqrt{13} \ units^2}$

6 0

3 years ago