14. Demostrar que \( x=\cos x \) para alguna \( x \) en \( \left(0, \frac{\pi}{2}\right) \) 15. Demostrar que \( x 2^{x}=1 \) para alguna \( x \) en \( (0,1) \)

Los intervalos de crecimiento de la función \( f(x)=2 x^{3}-3 x^{2}+12 x+7 \), son: a. \( (-\infty,-2) \cup(1, x) \) b. \( (-\infty,-2) \cup(2, \infty) \) c. \( (-\infty,-1) \cup(2, \infty) \) d. \( (-1,2) \cup(2, \infty) \)

5)- Calcula la derivada segunda de: \( f(x)=\sqrt{\ln x^{2}} \)

47) \( f(x)=3 x^{3}-5 x^{2}+15 x-25 \) A) \( \left\{-\frac{7}{3}, i \sqrt{5},-i \sqrt{5}\right\} \) B) \( \left\{\frac{5}{3}, i \sqrt{6},-i \sqrt{6}\right\} \) C) \( \left\{\frac{5}{3}, \frac{i \sqrt{10}}{2},-\frac{i \sqrt{10}}{2}\right\} \) D) \( \left\{\frac{5}{3}, i \sqrt{5},-i \sqrt{5}\right\} \)

A ball is thrown from a height of 40 meters with an initial downward velocity of \( 10 \mathrm{~m} / \mathrm{s} \). The ball's height \( h \) (in meters) after \( t \) seconds is given by the following. \[ h=40-10 t-5 t^{2} \] How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)

49) \( f(x)=-x^{3}+3 x^{2}+3 \)