Answer:
This contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3
Step-by-step explanation:
The given function is
When we differentiate this function with respect to x, we get;
We want to find all values of c in (1,7) such that f(7) − f(1) = f '(c)(7 − 1)
This implies that;
![c-3=\sqrt[3]{63.15789}](https://tex.z-dn.net/?f=c-3%3D%5Csqrt%5B3%5D%7B63.15789%7D)
![c=3+\sqrt[3]{63.15789}](https://tex.z-dn.net/?f=c%3D3%2B%5Csqrt%5B3%5D%7B63.15789%7D)
If this function satisfies the Mean Value Theorem, then f must be continuous on [1,7] and differentiable on (1,7).
But f is not continuous at x=3, hence this hypothesis of the Mean Value Theorem is contradicted.
Answer:
y = 7x - 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (1, - 3)
m = 
= 
= 7, thus
y = 7x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 4), then
4 = 14 + c ⇒ c = 4 - 14 = - 10
y = 7x - 10 ← equation of line
Answer:
12
Step-by-step explanation:
The correct answer is A.
Horizontal shift is obtained by addition/subtraction a number to every occurrence of x in the equation. Addition indicates a shift towards left and subtraction indicates a shift towards right.
So the correct answer is Subtract that number From.
Answer:
240 miles
Step-by-step explanation:
he drives 30 miles there and back which is 60 miles and 6 times 4 is 24 so 60 times 4 is 240
