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:
The slope of a line that has a y-intercept but no x-intercept will be zero.
Step-by-step explanation:
If the line has no x-intercept, then it never intersects the x-axis, so it must be parallel to the x-axis.
If a line does not have an x-intercept, it means it would never intersect the x-axis.
Thus, it must be parallel to the x-axis, meaning its slope will be zero. It would be just a horizontal line.
For example, y=9 is the line equation that does not have an x-intercept and its slope is zero.
Therefore, the slope of a line that has a y-intercept but no x-intercept will be zero.
Answer:
She can only make 5/6 of her recipe with the amount of milk that she has.
Step-by-step explanation:
Some data of this problem is missing, the data missing is:
Her recipe calls for 3/4 of a pint of milk and she only has 5/8 of a pint of milk.
Now, to know what's the portion she can do with that amount we need to divide the amount of milk she has by the total amount she needs:
÷
When we divide we turn the second fraction upside down (the numerator becomes the denominator and viceversa) and multiply, thus:
÷
×
If we simplify this last expression we have:
Thus, she can only make 5/6 of her recipe with the amount of milk that she has.
<em>Note: In case the data missing is different, you can apply this same procedure with the fractions you have. </em>
Answer:
r = 6 m
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r
Substitute in what we know
37.68 = 2 * 3.14 * r
37.68 = 6.28 r
Divide each side by 6.28
37.68/6.28 = 6.28 r/6.28
6 = r
