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:
see attached diagram
Step-by-step explanation:
First, draw the dashed line 50x+150y=1500 (dashed because the inequality is without notion "or equal to"). You can do it finding x and y intercepts.
When x=0, then 150y=1500, y=10.
When y=0, then 50x=1500, x=30.
Connect points (0,10) and (30,0) to get needed dashed line.
Then determine which region (semiplane) you have to choose. Note that origin's coordinates (0,0) do not satisfy the inequality 50x + 150y>1500, because
This means that origin lies outside the needed region, so you have to choose the semiplane that do not contain origin (see attached diagram).
Answer:
x divided by 4+3=8
Step-by-step explanation: quotient is the division part
Answer:
StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction
Step-by-step explanation:
It is stated that both triangles satisfy the Side Side Side (SSS) postulate, and the proportions between 2 sides are provided, therefore, the missing proportion is needed to prove that the triangles are similar, that proportion is: BC/YZ = 6/3
4 for #1
1.3 for #2
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