Find the derivative of the function \$y = 5x^7 + 3x^4 - 8x - 7\$.

A) \$12x^6 + 7x^3 + 5\$

B) \$35x^6 + 12x^3 - 8\$

C) \$12x^6 - 7x^3 - 5\$

D) \$35x^6 + 18x^3 - 8\$

Determine the equation for the line tangent to \$f(x) = x^4 - 18x^2 - 13\$ at x = 4.

A) \$y + 4 = 12(x - 3)\$

B) \$y + 5 = 12(x + 3)\$

C) \$y + 45 = 112(x - 3)\$

D) \$y - 45 = 112(x + 3)\$

Find the derivative of the function \$p(x) = (xsin^2(4x))/(\sqrt(x^4 - 2))\$.

A) \$((sin2(4x) + 8xsin(4x)cos(4x)) \sqrt(x^4 + 2) - (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 2)))/(x^4 + 2)\$

B) \$((sin2(4x) + 7xsin(4x)cos(4x)) \sqrt(x^4 - 2) + (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 2)))/(x^4 - 2)\$

C) \$((sin2(4x) + 8xsin(4x)cos(3x)) \sqrt(x^4 - 2) + (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 3)))/(x^4 - 2)\$

D) \$((sin2(4x) + 8xsin(4x)cos(4x)) \sqrt(x^4 - 2) - (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 2)))/(x^4 - 2)\$

Find the derivative of \$v(x) = (x cos(x))/(x^2 - 1)\$.

A) \$(-x^3 sin(x) - x^2 cos(x) + x sin(x) - cos(x))/(x^2 - 1)^2\$

B) \$(x^3 sin(x) - x^2 2cos(x) + x sin(x) - cos(x))/(x^2 + 1)^2\$

C) \$(-x^3 sin(x) - x^2 cos(x) + x sin(x) - 3cos(x))/(x^2 - 1)^2\$

D) \$(x^3 sin(x) + x^2 cos(x) + x sin(x) - cos(x))/(x^2 + 1)^2\$

Find the derivative of the function \$k(x) = x \sqrt(x^2 + 3)\$.

A) \$(2x^2 + 3)/(\sqrt(x^2 + 3))\$

B) \$(x^2 - 3)/(\sqrt(x^2 - 3))\$

C) \$(x^2 + 3)/(\sqrt(x^2 + 3))\$

D) \$(x^2 - 3)/(\sqrt(x^2 + 3))\$

Find the tangent line to \$f(x) = 7x^4 + 8x^-6 + 2x\$ at x = -1.

A) y = 22x + 35

B) y = 22x + 37

C) y = 22x - 35

D) y = 23x + 35

The position of an object at any time t is given by \$s(t) = 3t^4 - 40t^3 + 126t^2 - 9\$. Determine the velocity of the object at any time t.

A) \$s(t) = 12t^3 - 120t^2 + 252t\$

B) \$s(t) = 12t^2 - 122t^2 + 252t\$

C) \$s(t) = 12t^3 - 120t^3 + 253t\$

D) \$s(t) = -12t^2 - 120t^2 + 252t\$

Determine where the function \$h(z) = 6 + 40z^3 - 5z^4 - 4z^5\$.

A) Increasing = 3 < z < 0, 0 < z < 2
Decreasing = ∞ < z < 3, 2 < z < ∞

B) Increasing = -3 < z < 0, 0 < z < 2
Decreasing = -∞ < z < -3, 2 < z < ∞

C) Increasing = z < -3 < 0, 0 < z < -2
Decreasing = -∞ < z < -3, 2 < z < ∞

D) Increasing = -3 < z < 0, 0 < z < 2
Decreasing = -∞ < -3 < z, 2 < z < ∞

Determine where, if anywhere, the tangent line to \$f(x) = x^3 - 5x^2 + x\$ is parallel to the line y = 4x + 23.

A) y = 5x + 32

B) y = -5x + 32

C) y = 4x + 23

D) y = -4x + 23

Find the derivative of \$f(x) = 3x^2 + 5x - 2\$.

A) \$f(x) = 6x - 5\$

B) \$f(x) = 6x + 7\$

C) \$f(x) = 6x + 9\$

D) \$f(x) = 6x + 5\$