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
#SPJ1
Confusing question but I would get 0, as if you have 4cm, that squared = 16cm^2. Therefore if it were increasing anymore, then you would not be able to get a value of 16.
A graph shows the roots to be
{-4, 3, 6}.
Answer:
X = 4
Step-by-step explanation:
x2 + 1 = 9
We have to cross 1 over to the other side so that x becomes a value on its own. Because we are it over, the addition sign changes to subtraction which makes the expression,
x2 = 9- 1
x2 = 8
For x to stand alone we have to divide both sides by 2
x 2/2 = x
and 8/2 = 4
Therefore x=4 (Answer)
Given:
The radius of the sphere is 6 in.
To find:
The volume of the sphere.
Solution:
We know that, the volume of a sphere is
Where, r is the radius of the sphere.
Putting r=6, we get
The volume of the sphere is 904.78 inches cubed.
Therefore, the correct option is C.
