Question #100202
For what value of x is the tangent of the graph of the function f (x) = x4− ax 3−4 parallel to the x axis?
1
Expert's answer
2019-12-10T11:06:31-0500

From the geometric interpretation of derivative it follows that a tangent line to the graph of the function f(x)f(x) at the point (x0,f(x0))(x_0,f(x_0)) is parallel to the xx axis if, and only if f(x0)=0.f'(x_0) = 0.

Then, we have the equation

f(x)=(x4ax34)=4x33ax2=x2(4x3a)=0f'(x) = (x^4 - ax^3 - 4)' = 4x^3 - 3ax^2 = x^2(4x - 3a) = 0

It has two solutions: x1=0,  x2=34a.x_1 = 0,\; x_2 = \frac{3}{4}a.


Answer: Either x=0x=0 or x=34a.x = \frac{3}{4}a.


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