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3 years ago

3. Find the slope of the line f(x)1/2x+8. Describe how the line slopes.

Mathematics

1 answer:

wariber [46]3 years ago

7 0

Answer:

slope: $\frac{1}{2}$

Step-by-step explanation:

$f(x)=mx+b\\m=slope\\\\f(x)=\frac{1}{2} x+8\\\frac{(rise)}{(run)}=\frac{1}{2}$

the linear line has a positive slope that goes up by 1 unit and right by 2 units

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$f'(x) = \frac{4x}{2x^2+1}$

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General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

f(x) = ln(2x² + 1)

Step 2: Differentiate

Derivative ln(u) [Chain Rule/Basic Power]: $f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}$
Simplify: $f'(x) = \frac{1}{2x^2+1} \cdot 4x$
Multiply: $f'(x) = \frac{4x}{2x^2+1}$

Step 3: Domain

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.

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