Answer:
Step-by-step explanation:
(x - 2)(x² + 7x + 4) = x(x² + 7x + 4) - 2*(x² + 7x + 4)
= x*x² + x*7x + 4*x - 2*x² -2* 7x -2* 4
= x³ + 7x² + 4x - 2x² -14x -8
= x³ + <u>7x² - 2x²</u> <u>+ 4x - 14x</u> - 8
= x³ + 5x² - 10x - 8
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:he melted
Step-by-step explanation: winters a good time to stay in and cuddle but put me in summer and i'll be a happy snow man
Answer:
You find it by finding the dimensions of the X up and down, and Y left and right
Step-by-step explanation:
