What is the x-coordinate of the point of inflection on the graph of #y=1/10x^(5)+1/2X^(4)-3/10#?

Answer 1

The x-coordinate of the inflexion point is #-3#

#y=1/10x^5+1/2x^4-3/10#
#(dy)/(dx)=1/2x^4+2x^3#
#(d^2y)/(dx^2)=2x^3+6x^2#
For second derivative, #(d^2y)/(dx^2)=0#
#2x^3+6x^2=0# #2x^2(x+3)=0# #x=0# or #x=-3#
Then you must these points for concavity Test #(0,-3/10)# When #x=-1#, #(d^2y)/(dx^2)=4# When #x=0#, #(d^2y)/(dx^2)=0# When #x=1#, #(d^2y)/(dx^2)=8# Therefore, #(0,-3/10)# is not a point of inflexion as the concavity doesn't change
Test #(-3,15 9/10)#, When #x=-4#, #(d^2y)/(dx^2)=-32# When #x=-3#, #(d^2y)/(dx^2)=0# When #x=-2#, #(d^2y)/(dx^2)=8# Therefore, #(-3,15 9/10)# is a point of inflexion as the concavity changes
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Answer 2

To find the x-coordinate of the point of inflection, you need to find the second derivative of the function, set it equal to zero, and solve for x. Then, plug that value into the original function to find the corresponding y-coordinate. So, first, find the second derivative of (y = \frac{1}{10}x^5 + \frac{1}{2}x^4 - \frac{3}{10}), which is (y'' = 12x^2 + 24x). Setting this equal to zero, we get (12x^2 + 24x = 0). Solving for x, we find (x = -2, 0). Then, plug these x-values into the original function to find the corresponding y-coordinates. Therefore, the x-coordinates of the points of inflection are (x = -2) and (x = 0).

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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.

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.

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.

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.

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