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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These are pretty easy once you get the concept.
think of <em>random letter</em> (x) as the term y, so in the case of p(x)=-3+4x, its just asking what is y when x equals all those values.
so p(-2) = -3 + 4(-2), since its asking to plug in -2 for x, which equals -11
p(0) = -3 + 4(0)
= -3
p(5) = -3 + 4(5)
= 17
Well they give you the equation and they want you to solve for time given that you know the amount of water in the tank. They tell you T=274 and that
T=450-8m so using the value T=274 in the equation to the left gives you:
274=450-8m subtract 450 from both sides
-176=-8m divide both sides by -8
22=m
So 22 minutes have passed when there is 274L remaining...
Answer:
Your coordinates would be:
(1,8) (1,5) (5,8)
Hope this helps!
I’m not entirely sure, but i do think it could be B.
