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Yuri [45]
2 years ago
6

For the function f(x)=ax^3+bx^2-5x+9, determine the values of a and b so that f(-1)=12 and f'(-1)=3

Mathematics
1 answer:
Alecsey [184]2 years ago
4 0

If

<em>f(x)</em> = <em>ax</em> ³ + <em>bx</em> ² - 5<em>x</em> + 9

then

<em>f '(x)</em> = 3<em>ax </em>² + 2<em>bx</em> - 5

Given that <em>f</em> (-1) = 12 and <em>f</em> '(-1) = 3, we get the system of equations

-<em>a</em> + <em>b</em> + 5 + 9 = 12

3<em>a</em> - 2<em>b</em> - 5 = 3

or

-<em>a</em> + <em>b</em> = -2

3<em>a</em> - 2<em>b</em> = 8

Multiply through the first equation by 2 and add it to the second one to eliminate <em>b</em> and solve for <em>a</em> :

2(-<em>a</em> + <em>b</em>) + (3<em>a</em> - 2<em>b</em>) = 2(-2) + 8

-2<em>a</em> + 2<em>b</em> + 3<em>a</em> - 2<em>b</em> = -4 + 8

<em>a</em> = 4

Substitute this into the first equation above to solve for <em>b</em> :

-4 + <em>b</em> = -2

<em>b</em> = 2

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3 years ago
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marta [7]

Answer:

0

Step-by-step explanation:

1) Multiply the first equation by -3:  -6x - 3y = 12

2) Substitute 2x + 12 for -3y in the above equation, obtaining:

-6x + 2x + 12 = 12

Then -4x = 0, and x = 0.  Letting x = 0 in the first equation, we get:

0 + y = -4, so y = -4.

The x-value at the intersection of the lines is zero (0).

That intersection is at (0, -4).

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3 years ago
What is 66.2% of 5071
crimeas [40]
To find the percentage of a number, you multiply it by the decimal the percentage is correlated to. In this case 66.2 % is equal to .662

5071x .662 is <span>3357.002.

Therefore, 66.2 % of 5071 is 3357.002

</span>
3 0
3 years ago
Read 2 more answers
Write a function g with the<br> parent function f(x) = x4 that has a vertex<br> at (3, -6).
Irina18 [472]

Answer:

g(x)=(x-3)^4-6

Step-by-step explanation:

The parent function is f(x)=x^4.

We want to transform this function so that its vertex will move from the origin to (3,-6).

In other words, we translate the parent function 3 units to the right and 6 units down,

Let g(x) be the new function then:

g(x)=f(x-3)-6

\implies g(x)=(x-3)^4-6

5 0
3 years ago
Start time 7:30 pm elapsed time _ end time 9:29 pm
user100 [1]
 what r u asking so I help you 
6 0
3 years ago
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