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.

Here we go ~
In the above question, it is given that :

A.) Find f(2) :


or

B.) Find
:

so, we can write it as :



Now, put x =
, and y = x and we will get our required inverse function ~

C.) Find
:



Answer:
To find the equation of the line parallel to the graph, first of all find the slope of the graph by making y the subject of the formula and comparing the resulting equation with y = mx + c , knowing fully well that m stands for the slope.
So, from the equation of the graph give, y = 4x/5 +1/5, therefore the slope is 4/5. For a line to be parallel to the graph then they must have the same slope, to find the equation of the line at the given point, then we use the formula
y - y1 = m ( x - x1 )
y - 3 = 4/5 ( x - 1 )
multiply through by 5
5( y - 3 ) = 4 ( x - 1)
5y - 15 = 4x - 4
5y - 4x = - 4 + 15
so, 5y - 4x = 11 is the equation
Step-by-step explanation:
The answer to this question would be 3d-2=31 and d=11