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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Answer:
Or if you want with the value of h too.
Step-by-step explanation:
Find the value of h and k by using the formula.
From y = x²-2
Substitute these values in the formula.
Therefore, h = 0.
Therefore, k = - 2.
From the vertex form, the vertex is at (h, k) = (0,-2). Substitute h = 0, a = 1 and k = -2 in the equation.
These type of equation where b = 0 can also be both standard and vertex form.
Answer: 13
Step-by-step explanation: Alright with the median you take all the numbers "11, 20, 17, 8, 8, 9, 20, 13, 21" and put them in numerical order. "8, 8, 9, 11, 13, 17, 20, 20, 21" Then the middle one is the median, since there are 9 numbers you take the fifth one. In this case it is 13. (Only knew the first one since I have no idea what they mean by quartiles)
Answer: 1.47
Step-by-step explanation:
-1.47 is negative, so the opposite would be positive 1.47. When you need the oppostite of something, you just put the opposite sign in front of it. In this case, a positive sign is invisible, so it would just be 1.47
For this case we have the following function:
To find the maximum of the function, what we should do is to derive the equation.
We have then:
We match zero:
We clear the value of x:
We substitute the value of x in the function to find the maximum:
Rewriting:
Answer:
a formula in terms of a for the maximum of f (x) is:
