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djyliett [7]
1 year ago
13

Find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1

Mathematics
1 answer:
kicyunya [14]1 year ago
6 0

Given:

f^{\prime}\left(x\right)=x-4,\text{ and}f\left(2\right)=-1

To find:

The correct function.

Explanation:

Let us consider the function given in option D.

f(x)=\frac{x^2}{2}-4x+5

Differentiating with respect to x we get,

\begin{gathered} f^{\prime}(x)=\frac{2x}{2}-4 \\ f^{\prime}(x)=x-4 \end{gathered}

Substituting x = 2 in the function f(x), we get

\begin{gathered} f(2)=\frac{2^2}{2}-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}

Therefore, the given conditions are satisfied.

So, the function is,

f(x)=\frac{x^{2}}{2}-4x+5

Final answer: Option D

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The product of two consecutive integers is 5 more than three time the larger. What are the integers?
kvasek [131]
When calculating consecutive integers, the smaller number is x and the larger number is (x + 1).
So the equation you can use is x + (x + 1) = 5 + 3(x + 1)
This is because the sum of the consecutive integers are equal to 5 more than 3 times the larger integer.
Now simplify:
x + (x + 1) = 5 + 3(x + 1)
2x + 1 = 5 + 3(x + 1)
2x + 1 = 5 + 3x + 3
2x + 1 = 3x + 8
Now isolate the variable:
2x + 1 = 3x + 8
Subtract 2x from both sides:
1 = x + 8
Subtract 8 from both side:
-7 = x
x = -7
So the smaller number is -7 and the larger number is -6.

Now check your answer:
-7 + (-7 + 1) = 5 + 3(-7 + 1)
-7 + (-6) = 5 + 3(-7 + 1)
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This works!

So the integers are -7 and -6.
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