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:
∠ ABC = 81° , ∠ FEC = 90°
Step-by-step explanation:
Since AB ≅ BC then Δ ABC is isosceles.
The median BE is therefore
The angle bisector of ∠ ABC and
BE bisects AC at right angles.
Thus
∠ ABE = ∠ CBE = 40° 30' , then
∠ ABC = 2 × 40° 30' = 81°
Since BE is perpendicular to AC then
∠ FEC = 90°
The answer is C because 24 times 10 to the 5th power is the same as 100,000 times 24
Ten times 45 is equal to 450
In the simplest form it looks like this:
<span><span>
−8</span>j</span>+<span>5
Hope this helped</span>
