What are the points of inflection, if any, of #f(x)=4x^3+15x^2150x+4 #?
Inflection point is at
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To find the points of inflection, you need to first find the second derivative of the function, f(x). Then, solve for the values of x where the second derivative equals zero or is undefined. After obtaining these xvalues, plug them into the original function to find the corresponding yvalues. The points (x, y) obtained will be the points of inflection, if any.

First derivative of f(x): f'(x) = 12x^2 + 30x  150

Second derivative of f(x): f''(x) = 24x + 30

Set f''(x) = 0 and solve for x: 24x + 30 = 0 x = 30/24 = 5/4

Plug x = 5/4 into the original function to find the corresponding yvalue: f(5/4) = 4(5/4)^3 + 15(5/4)^2  150(5/4) + 4

Calculate f(5/4) to find the ycoordinate of the point of inflection, if any.
The point of inflection, if it exists, would be (5/4, y).
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
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