  Find all the value(s) of x at which f(x)=4x33−7x22−15x+10 has a horizontal tangent line. If there is more than one answer, give all of the x-values separated by commas, e.g. if f(x) has a horizontal tangent line at x=3 and x=5 enter 3,5.

Question

Find all the value(s) of x at which f(x)=4x33−7x22−15x+10 has a horizontal tangent line. If there is more than one answer, give all of the x-values separated by commas, e.g. if f(x) has a horizontal tangent line at x=3 and x=5 enter 3,5.

Step 1

Given the curve y=f(x)=4x^3-7x^2-15x+10. To determine at what points the tangent is parallel to the x-axis

Step 2

Given the curve y=f(x), the slope of the tangent  at any point x=a is the derivative f'(a). So, the tangent is horizontal (parallel to the x-axis ) at x=a if and only if the derivative f'(a)=0.

Step 3

So, to find the required points, we solve t...

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