All categories

2 years ago

Let f(x) = e ^3x/5x − 2. Find f'(0).

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

4 0

Answer:

Step-by-step explanation:

Our friend asking what the actual function is has a point. I completed this under the assumption that what we have is:

$f(x)=\frac{e^{3x}}{5x-2}$ and used the quotient rule to find the derivative, as follows:

$f'(x)=\frac{e^{3x}(5)-[(5x-2)(3e^{3x})]}{(5x-2)^2}$ and simplifying a bit:

$f'(x)=\frac{5e^{3x}-[15xe^{3x}-6e^{3x}]}{(5x-2)^2}$ and a bit more to:

$f'(x)=\frac{5e^{3x}-15xe^{3x}+6e^{3x}}{(5x-2)^2}$ and combining like terms:

$f'(x)=\frac{11e^{3x}-15xe^{3x}}{(5x-2)^2}$ and factor out the GFC in the numerator to get:

$f'(x)=\frac{e^{3x}(11-15x)}{(5x-2)^2}$ That's the derivative simplified. If we want f'(0), we sub in 0's for the x's in there and get the value of the derivative at x = 0:

$f'(0)=\frac{e^0(11-15(0))}{(5(0)-2)^2}$ which simplifies to

$f'(0)=\frac{11}{4}$ which translates to

The slope of the function is 11/4 at the point (0, -1/2)

You might be interested in

PLEASE HELP ASAP!!! 98 POINTS FOR ONE MULTIPLE CHOICE QUESTION!!! I DO NOT HAVE PICTURES BUT ANYONE IN FLVS PLEASE ANSWER!!!

sladkih [1.3K]

y = −2x + 13

y = 2x − 3

Set the equations to equal and solve for x:

-2x + 13 = 2x -3

Add 2X to each side:

13 = 4x -3

Add 3 to each side:

16 = 4x

Divide both sides by 4:

x = 16/4

x = 4

Now replace x with 4 in one of the equations and solve for y:

y = -2(4) +13

y = -8 +13

y = 5

x = 4 and y = 5 , which is the ordered pair (4,5)

Both numbers are positive values, so the second graph is correct.

5 0

3 years ago

Read 2 more answers

A forest covers 71,000 acres. A survey finds that 0.3% of the forest is old-growth trees. How many acres of old-growth trees

Sauron [17]

Answer:

213 acres

Step-by-step explanation:

5 0

3 years ago

What is the answer for 2ab(xa^9+ya^3-6)

trapecia [35]

The answer for 2ab(xa^9+ya^3-6) is 2a^10bx + 2a^4by-6ab.

What is the mathematical expansion?

A mathematical expansion can be described as the finite combination of symbols which can be seen as one having rules which is usually based on the context that is been used.

The solution for the question is 2a^10bx + 2a^4by-6ab

Therefore, the expansion of 2ab(xa^9+ya^3-6) is 2a^10bx + 2a^4by-6ab.

Learn more about expansion at:

brainly.com/question/723406

8 0

2 years ago

State the gradient and the y-axis intercept of y=3x+7

Damm [24]

3

The 3 is the gradient in front of the x

Mark brainliest please

8 0

3 years ago

Read 2 more answers

Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a t

Archy [21]

Answer:

You need 4 weights, and the weights are 1; 3; 9 and 27.

Step-by-step explanation:

Since the scale has two plates, we can place weights on either side and also the object so it can be balanced.

This is a key part of the problem, it's not only on the other side of the scale, but on both sides.

Let's do the math now.

If i get two weights, 1 and 3. I can form this combinations.

Object of 1lb = 1

Object of 2lb + 1 weight = 3 weight.

Object of 3lb = 3 weight

Object of 4lb = 1 weight + 3 weight.

So what if i want to add the next weight and that weight to add me the maximum amount of objects. The weight would have to have a difference with the last object plus one. So if i grab 9. 9 minus 4 is 5. And that is a difference with the last object plus 1.

With a weight of 9, now i can add all the integers up to 13lb.

And the next step? Lets add one more. Keeping the last rule, the weight would have to have a difference with the last object plus one. So if i grab 27, 27 minus 13 is 14. And that is a difference witht the last object plus 1.

The sum of all the weights adds up to 40 pounds. And i can balance any integer in the middle.

The formula we are using is p – n = n + 1

Where p is the new weight. and n is the last object we weighted. And the sum of the weights goes up to the last object we can place on the scale, and in this case is 40.

4 0

3 years ago