Answer:
12 cups of sugar
Step-by-step explanation:
i hope it right
Answer:
{-2, -14, -26, -50}
Step-by-step explanation:
The range of the function is the function evaluated at each point of the given domain. So to find the range of the function we need to find the value of the function for each point in the domain:
- For x = -8
The first value of the range of the function is -2
- For x = -2
The second value of the range is -14
- For x = 4
Th third values of the range is -26
- For x = 16
The fourth and last value of the range is -50
Now we can put all the values of the range together
The range of the function is {-2, -14, -26, -50}
Using derivatives, it is found that regarding the tangent line to the function, we have that:
- The equation of the line is y = 962x - 5119.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:
f(x) = 5x³ + 2x + 1.
The derivative is given by:
f'(x) = 15x² + 2.
Hence the slope at x = 8 is:
m = f'(8) = 15(8)² + 2 = 962.
The line goes through the point (8,f(8)), hence:
f(8) = 5(8)³ + 2(8) + 1 = 2577.
Hence:
y = 962x + b
2577 = 962(8) + b
b = -5119.
Hence the equation is:
y = 962x - 5119.
More can be learned about tangent lines at brainly.com/question/8174665
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