(Solved): may you guys do number 7 and 8 asap please  6. A point moves along the curve \( y=2 x^{2}-1 \) ...

6. A point moves along the curve \( y=2 x^{2}-1 \) in such a way that the \( y \) value is decreasing at the nate of 2 units \( p \) e second. At what rate is \( x \) changing when \( x=-\frac{3}{2} \) ? a. decrrasing \( \frac{7}{2} \) univsec d. decreasing \( \frac{1}{3} \) unit/sec b. increasing \( \frac{7}{2} \) unit/sec c. Nooe of these c. increasing \( \frac{1}{3} \) unit/sec 7. Find the absolute maximam and absolute minimum of \( f \) on the interval \( (0,3] . f(x)=\frac{x^{3}-4 x^{2}+7 x}{x} \) a. Maximum: None Minimume \( (3,4) \) d. Maximum \( (0,7) \) Minimum \( (2,3) \) b. Maximum: \( (0,7) \) Minimum \( (3,4) \) c. None of these c. Maximum: None Minimum \( (2,3) \) 8. Find the absolute maximum and absolute minimum of \( f \) on the intenal \( (-4,-1] \cdot f(x)=\frac{x^{3}+8 x^{2}+19 x+12}{x+4} \) a. Maximum None Minimum \( (-2,-1) \) d. Maximum: None Minimum \( (-1,0) \) b. Maximum: \( (-4,3) \) Minimum \( (-1,0) \) c. Nonc of these c. Maximum \( (-4,3) \) Minimmem \( (-2,-1) \) 9. Given \( f(x)=9-\frac{14}{x} \), find all the \( c \) in the interval \( (2,7) \) weh that \( f^{\prime}(c)=\frac{f(7)-f(2)}{7-2} \). 9 d. \( \frac{14}{9} \) b. increasing \( \frac{1}{2} \) unit/sec c. None of these c. increasing \( \frac{1}{3} \) unit/sec 7. Find the absolute maximum and absolute minimum of \( f \) on the interval \( (0,3] . f(x)=\frac{x^{3}-4 x^{2}+7 x}{x} \) a. Maximum: None Minimum \( (3,4) \) d. Maximum: \( (0,7) \) Minimum \( (2,3) \) b. Maximum: \( (0,7) \) Minimum \( (3,4) \) c. None of these c. Maximum: None Minimum \( (2,3) \) 8. Find the absolute maximum and absolute minimum of \( f \) on the interval \( (-4,-1], f(x)=\frac{x^{3}+8 x^{2}+19 x+12}{x+4} \) a. Maximumr None Minimum \( (-2,-1) \) d. Maximum: None Minimum \( (-1,0) \) b. Maximum: \( (-4,3) \) Minimum \( (-1,0) \) c. Nooe of these c. Maximum: \( (-4,3) \) Minimum \( (-2,-1) \) 9. Given \( f(x)=9-\frac{14}{x} \), find all the \( c \) in the interval \( (2,7) \) such that \( f^{\prime}(c)=\frac{f(7)-f(2)}{7-2} \). a. \( \frac{9}{2} \) d. \( \frac{14}{9} \) b. \( \pm \sqrt{14} \) c. None of these c. \( \sqrt{14} \)