The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
A)The y-intercept is 50 because when X=0, y=50. This shows that the car was moving at 50 mph as an initial speed.
B) in two hours (from 1 to 3) the speed increased by 4 miles per 2hours. (from 52 to 56). 4/2 = 2 mph, which is the average rate of change. This represents the amount of speed increased each hour.
C) y=2x+50, and y=60 in this case, so 60=2x+50
60=2x+50
-50 -50
-----------------
10=2x
5=x, so the domain is X<=5 (less than or equal to 5)
Answer:
x = 4
Step-by-step explanation:
It is given that 
, and we have to solve the given equation for x.
Now, we have
Squaring both sides we get
![[\sqrt{(x - 3)}] ^{2} = [\sqrt{x} + 3]^{2}](https://tex.z-dn.net/?f=%5B%5Csqrt%7B%28x%20-%203%29%7D%5D%20%5E%7B2%7D%20%3D%20%5B%5Csqrt%7Bx%7D%20%2B%203%5D%5E%7B2%7D)
⇒ x - 3 = x + 6√x + 9 {Since we know the formula of (a + b)² = a² + 2ab + b²}
⇒ 6√x = - 12
⇒ √x = -2
Again squaring both sides we get
⇒x = 4 (Answer)
Company A charges $75.50 and 14¢ per mile, then for x miles, Company A charges 75.5 + 0.14x dollars
Company B charges $30.50 and 9¢ per mile, then for x miles, Company B charges 30.5 + 0.09x dollars
Subtracting the second equation to the first one,
75.5 + 0.14x
-
30.5 + 0.09x
----------------------
45 + 0.05x
For x miles, Company A charges 45 + 0.05x dollars more than Company B.
Real quick so I can sleep. it is because obtuse is over 90 degrees
