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:
Step-by-step explanation:
5h-8=2h+19
5h-2h=19+8
3h=27
h=27/3
h=9
Answer:
2w + 2
Step-by-step explanation:
Width = w
Twice its width = 2*w =2w
2 inches more than twice its width = 2w + 2
Length = 2w + 2
Answer:
- Lena's Method: 280
- Jackson's Method: 280
Step-by-step explanation:
Lena's Method:
- 8 + 12 = 20
- Plug 20 in: 14(20)
- 14(20) = 14 × 20 = 280
Jackson's Method:
- 14 × 8 = 112
- 14 × 12 = 168
- Re-write the expression: 112 + 168
- 112 + 168 = 280
I hope this helps!
Answer:
Step-by-step explanation:
