Create a function that has a derivative of f(x) = 2x + 1 at a given input value of your choice.

Mathematics

1 answer:

madreJ [45]3 years ago

6 0

F(x) = (x^2) + x + C at (1,1)

1 = 1 + 1 + C

-1 = C

so,

F(x) = (x^2) + x - 1

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3 years ago

X+ 3/4 ≥ -1/3<br> Can I get help with this I need the work and answer.

andreev551 [17]

Solving this inequality is similar to solving a regular equation. The only thing you need to worry about with inequalities is that when you are dividing or multiplying by a negative number, you must flip the inequality sign. You won't have to worry about that here!

You are told x + 3/4 ≥ -1/3. Isolate the x by subtracting 3/4 from both sides. To subtract fractions, find a common denominator on both fractions, subtract the numerators, put the difference over the common denominator, and simplify if needed. The common denominator between $\frac{3}{4}$ and $- \frac{1}{3}$ is 12.
1) To make the denominator of $\frac{3}{4}$ , 12, multiply it by 3/3 (aka 1):
$\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}$

2) To make the denominator of $- \frac{1}{3}$ , 12, multiply it by 4/4:
$- \frac{1}{3} \times \frac{4}{4} = -\frac{4}{12}$

3) Subtract the fractions to find the inequality for x:
$x + \frac{3}{4} \geq - \frac{1}{3}\\
x + \frac{9}{12} \geq -\frac{4}{12}\\
x \geq -\frac{4}{12} - \frac{9}{12} \\
x \geq -\frac{13}{12}$

You answer is x ≥ -13/12, or if you want to make -13/12 a mixed number, x ≥ $-1 \frac{1}{12}$ .