Find the vertex of the given function. f(x) = |x – 5| + 10
2 answers:
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The value of the derivative of the function g(x) at x = 1 will be 1/3. Then the correct option is A.
<h3>What is an inverse function?</h3>A function that may convert into another function is known as an inverse function or anti-function.
If the function is f(x) = sinx + 2x + 1.
Then the derivative of an inverse function g(x) of a function f(x) at a given value (a) will be
The derivative of f(x) will be
f'(x) = cos x + 2
Then the given value of a will be
a = 1
g(x) = f⁻¹(x)
put x = 0, then we have
f(0) = sin 0 + 2(0) + 1
f(0) = 1
Put x = 1, in the function f⁻¹(x). Then we have
f⁻¹(1) = 0
and
g(1) = 0
Then put a = 1, then we have
More about the inverse function link is given below.
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Velocity, distance and time:
This question is solved using the following formula:
In which v is the velocity, d is the distance, and t is the time.
On the first day of travel, a driver was going at a speed of 40 mph.
Time , distance of
, v = 40. So
The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles
On the second day, the velocity is .
On the first day, he drove 2 more hours, which means that for the second day, the time is:
On the first day, he traveled 20 more miles, which means that for the second day, the distance is:
Thus
System of equations:
Now, from the two equations, a system of equations can be built. So
Find the total distance traveled in the two days:
We solve the system of equation for , which gets the distance on the first day. The distance on the second day is
, and the total distance is:
From the first equation:
Replacing in the second equation:
Thus, the total distance is:
The total distance traveled in two days was of 380 miles.
For the relation between velocity, distance and time, you can take a look here: brainly.com/question/14307500