What is the domain of this scatter plot?
1 answer:
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Answer:
1.49
Step-by-step explanation:
In order to find the slope of the tangent line to a given equation, and in a given point, we need to:
1. Find the first derivative of the given function.
2. Evaluate the first derivative function in the given point.
1. Let's find the first derivative of the given function:
The original function is
But remeber that the derivative of is
so,
2. Let's evaluate the first derivative function in the given point
The given point is (0.4,1.49) so:
Notice that the calculated slope of the tangent line is equal to the y-coordinate of the given point because f'(x)=f(x). In conclusion, the slope of the tangent line is equal to 1.49.
<h2>Steps:</h2>
So firstly, to factor this we need to first find the potential roots of this polynomial. To find it, the equation is , with p = the factors of the constant and q = the factors of the leading coefficient. In this case:
Next, plug in the potential roots into x of the equation until one of them ends with a result of 0:
Since we know that 3 is a root, this means that one of the factors is (x - 3). Now that we know one of the roots, we are going to use synthetic division to divide the polynomial. To set it up, place the root of the divisor, in this case 3 from x - 3, on the left side and the coefficients of the original polynomial on the right side as such:
- 3 | 1 - 10 + 25 - 40 + 84
- _________________
Firstly, drop the 1:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓
- _________________
- 1
Next, multiply 3 and 1, then add the product with -10:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3
- _________________
- 1 - 7
Next, multiply 3 and -7, then add the product with 25:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3 - 21
- _________________
- 1 - 7 + 4
Next, multiply 3 and 4, then add the product with -40:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3 - 21 + 12
- _________________
- 1 - 7 + 4 - 28
Lastly, multiply -28 and 3, then add the product with 84:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3 - 21 + 12 - 84
- _________________
- 1 - 7 + 4 - 28 + 0
Now our synthetic division is complete. Now since the degree of the original polynomial is 4, this means our quotient has a degree of 3 and follows the format . In this case, our quotient is
.
So right now, our equation looks like this:
However, our second factor can be further simplified. For the second factor, I will be factoring by grouping. So factor x³ - 7x² and 4x - 28 separately. Make sure that they have the same quantity inside the parentheses:
Now it can be rewritten as:
Since the polynomial cannot be further simplified, your answer is: