Function slope vanishes

Calculus Level 2

Let $f(x)$ be a multi differentiable function of $x$ . Find the value of $\dfrac1x$ , where the slope of the function $x f(x)$ is 0 with respect to $x$ .

-f(x)/f''(x) f(x) -f'(x)/f''(x) f'(x) -f'(x)/f(x)

1 solution

Prince Loomba
Feb 1, 2016

f(x)+f'(x)*x=0 by product rule.

Hey Prince Loomba, I know this is not relevant to this problem, but I tried your "Integrate 2" problem about the $arccos(sin(x^2))$ . I solved the integral, which was $\frac{\pi^3}{3} - \frac{5\pi^2}{2} + (\frac{\pi}{2})^{3/2}(\frac43-4\sqrt{3}+\frac{20}{3}\sqrt{5})$ . This agrees with the numerical integration on a calculator, but does not agree with your answer. Thought I'd let you know.

EDIT: The numerical integration and the value of that expression is 3.99445

Daniel Longenecker - 5 years, 3 months ago

Function slope vanishes

1 solution

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