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.
<u>Answer:</u>
The range of the function y = 2cos x is -2 <y < 2 .
<u>Step-by-step explanation:</u>
We know that cos (0) = 1 and cos (π) = - 1 are the two extreme values which cos x assume when x ∈ R and it is also that cos (x) is a continuous periodic function with period 2π when x ∈ R ,
since ,
cos (x + 2π) = cos x
So, the range of the function y = 2cos x is -2 <y < 2 .
The correct order is:
the probability of heads on 2nd and 4th toss only;
the probability of at least 3 tails in a row;
the probability of 3 or more heads;
the probability of consecutive tails; and
the probability of at least 2 tails.
There are 16 outcomes in the sample space.
There are 8 ways of having consecutive tails; this gives the probability 8/16.
There is 1 way of having heads on the 2nd and 4th toss only, making the probability 1/16.
There are 3 ways to have at least 3 tails in a row, making the probability 3/16.
There are 11 ways to have at least 2 tails, making the probability 11/16.
There are 5 ways to have at least 3 heads, making the probability 5/16.
