The slope of the line that is perpendicular to the tangent line at x=1 is, [tex]\frac{1}{4}[/tex]
Option E is correct.
Slope of line:
The derivative of given function with respect to x is known as slope of function.
Given function is, [tex]g(x)=-3x^{3}+5x-3[/tex]
Now differentiate the above function.
[tex]\frac{dg(x)}{dt}=-9x^{2} +5[/tex]
[tex]\frac{dg(x)}{dx}[/tex] at [tex]x=1[/tex] is,
[tex]\frac{dg}{dt} =-9(1)^{2}+5 =-4[/tex]
the slope of the line that is perpendicular to the tangent line at x=1 is,
Slope[tex]=-\frac{1}{dg/dx}=\frac{1}{4}[/tex]
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