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:
x = 8/7
Step-by-step explanation:
log (X + 8) = log x + log 8
We know that log a + log b = log ab
log (X + 8) = log 8x
Raise each side to base 10
10^log (X + 8) = 10^log 8x
x+8 = 8x
Subtract x from each side
x+8-x = 8x-x
8 = 7x
Divide by 7
8/7 = 7x/7
8/7 =x
Answer:
90
Step-by-step explanation:
It starts going up by 6. Then it goes up by 2 more than six. 6, 8, 10. Going up 2 more than last time. 2018 would be 12 more, or 76, and 2019 would be 14 more, or 90.
Composite because number that are greater than 5 are composite