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1 year ago

If f(x) = f(x)g(x), where f and g have derivatives of all orders, show that f'' = f ''g + 2f 'g' + fg''.

1 answer:

5 0

Differentiating once, we have

$f'(x)=f'(x)g(x)+f(x)g'(x)$

Differentiating again,

$f''(x)=f''(x)g(x)+f'(x)g'(x)+f'(x)g'(x)+f(x)g''(x)$
$f''(x)=f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x)$

as needed.

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Evaluate. 58−(14)2=58-142= ________

nasty-shy [4]

For this case we have the following expression:

$58- (14) ^ 2$

The first step is to solve the quadratic term.

We have then:

$58- (14) ^ 2 = 58-196$

Then, the second step is to subtract both resulting numbers:

$58- (14) ^ 2 = -138$

We observe that the result obtained is a negative number.

Answer:

The result of the expression is given by:

$58- (14) ^ 2 = -138$

7 0

1 year ago

Which of the following notations correctly describe the end behavior of the polynomial graphed below?

algol13

The right answer is C

Let me to explain. From the graph we know that the vertex of this parabola is $V(0,8)$ . This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative. Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right. In a mathematical language this is:

$x \rightarrow -\infty, f(x) \rightarrow -\infty \\ \\ x \rightarrow \infty, f(x) \rightarrow -\infty$

4 0

1 year ago

Work this travel problem based on the data provided in the various tables in this section.

grigory [225]

42% ................................

3 0

1 year ago

A jar contains three marbles; 1 yellow (y), 1 orange (o), and 1 red (r). Which list shows all the possible outcomes for choosing

Zarrin [17]

Answer:

see below

Step-by-step explanation:

Since we replace the marble , we can draw the same color again

yy oo ro

yo oy ry

yr or rr

There are 9 possible outcomes for drawing 2 marbles

5 of them have at least one yellow marble

4 1

2 years ago

Read 3 more answers

a teapot is 1/3 full of tea. When all of the tea is poured into an empty container, the container is 2/3 full. what fraction of

motikmotik

(1/3)t = (2/3)c, where "t" is for teapot and "c" is for the container.
Multiply both sides by (3/2) in order to get 1 on the right-hand side.
(3/2)(1/3)t = (3/2)(2/3)C
simplify the equation to get the answer which is:
(1/2) teacup = 1 full container.
Hope this helps :)

4 0

1 year ago