Question #f36b9

1 Answer
Jan 25, 2018

Answer:

Refer explanation.

Explanation:

Given -

#y=x^4+8x^3#

To graph, a function, first find the turning points.
Find the first derivative and set it to zero, so that you know the value of #x#, the slope of the curve becomes zero.

#dy/dx=4x^3+24x^2#

#dy/dx=0=>4x^3+24x^2=0#

#4x^2(x+6)=0#

#4x^2=0#

#x=0#

#x=-6#

At #x=0# and at #x=-6#, there are turning points.
Take a range of values that includes 0 and -6. Calculate the corresponding value of #y#. Tabulate them. Use the pair of the points to obtain the curve.

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At #x=0#, there is a point of inflexion.
At #x=-8#, the curve reaches the minimum.