A turning point occurs when the velocity is equal to zero, but the acceleration is not equal to zero.
t(x)=(x+5)^3+7
dt/dx=3(x+5)^2
d2t/dx2=6(x-5)
dt/dx=0 only when x=-5
However, since d2t/dx2(-5)=0, this point is an inflection point, not a turning point.
So there is no turning point for this function.
Now in this problem, it is even easier than the above to show that there is no turning point. A turning point by definition is when the derivative or velocity changes sign. Since in this case v=3(x+5)^2, for any value of x, v≥0, and thus never becomes negative, so it never changes from a positive to negative velocity because velocity in this instance is a squared function.
His commission is simply: $15,000 x 0.04 = $600
Answer:
Step-by-step explanation:
<u>Given equation</u>
- f(t) = 2^(kt)
- f - number of cells, t - number of months, k- coefficient
<u>We got 32 cells in the first month. It means:</u>
<u>Using these numbers we can find the coefficient k:</u>
- 32 = 2^(k*1)
- 2^5 = 2^k
- k = 5
<u>Then the equation becomes:</u>
<u>Average time is 9 months, we can calculate the number of cells:</u>
- f(9) = 2^(5*9) = 2^45 ≈ 3.5*10^13
A% x 50 = 35
a/100 x 50 = 35
a/2 = 35
a = 70
