How do you find the y coordinate of the inflection point of the function #f(x)= 10(x-5)^3+2#?

Answer 1

A function's inflection points are the zeroes of its second derivative where its sign changes.

Now let us calculate the second derivative:

#y'=30(x-5)^2#

and

#y''=60(x-5)#.

Ther is only one zero: #x=5# and the second derivative change in sign in it, so #P(5,2)# is the only inflection point, as you can see from the graph:

chart{10(x-5)^3 +2 [-10, 10, -5, 5]}

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Answer 2

Ezra Adams

To find the y-coordinate of the inflection point of the function ( f(x) = 10(x - 5)^3 + 2 ), you first need to find the second derivative of the function, ( f''(x) ). Then, set the second derivative equal to zero and solve for ( x ). Once you have the ( x )-coordinate of the inflection point, plug it back into the original function to find the corresponding ( y )-coordinate.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.