What is the equation of the normal line of $f (x) = e^{2 x} - x^{3}$ $f(x)=e^(2x)-x^3$ at $x = 2$ $x=2$ ?

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Answer 1 · 2016-07-18T10:46:08

$\approx - 0.01$ $~~ -0.01$

We know that the slope of the tangent at $x = 2$ $x = 2$ is $f'(2)$ . Now

$f'(x) = 2 e^{2 x} -3 x^2$

so that

$f'(2) = 2 e^4-12~~97.2$

Thus the slope of the line normal to this is $-1/97.2 ~~ -0.01$

What is the equation of the normal line of f(x)=e^(2x)-x^3f(x)=e2x−x3f(x)=e^(2x)-x^3 at x=2x=2x=2?