The line of symmetry.
It divides the parabola into to halves that are exactly the same.
Answer:
To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.
Step-by-step explanation:
As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.
To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:
dfdx=4x−3
f(b)−f(a)b−a=f'(c)
f(x)x=0=1
f(x)x=2=3
Hence:
3−12=4c−3
and c=1.
Answer:
slope = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = 
with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 7)
m = 
= 
= 2
