Quiz about Higher Order Derivatives Review

Question 1

Given that $$f\left(x\right)=2x^4-3x^3+4x^2$$ what is $$f^{$$ ?

Accepted Answer

$$48x-18$$

Answer

$$8x^3-9x^2+8x$$

Answer

$$24x^2-18x+8$$

Answer

$$48$$

Question 2

Suppose $$f\left(x\right)=x^7-x^6+x^5$$ what is $$f^4\left(x\right)$$ ?

Accepted Answer

$$840x^3-360x^2+120x$$

Answer

$$210x^4-120x^3+60x^2$$

Answer

$$42x^5-30x^4+20x^3$$

Answer

$$7x^6-6x^5+5x^4$$

Question 3

If $$h\left(x\right)=2x^6-3x^5+4x^4$$ , find $$f^4\left(x\right)$$

Accepted Answer

$$720x^2-360x+96$$

Answer

$$12x^5-5x^4+16x^3$$

Answer

$$60x^4-60x^3+48x^2$$

Answer

$$240x^3-180x^2+96x$$

Question 4

Find $$k^{$$ if $$k\left(x\right)=8x^{-3}-24x^{-2}+12x^{-1}$$

Accepted Answer

$$96x^{-5}-144x^{-4}+24x^{-3}$$

Answer

$$0$$

Answer

$$-480x^{-6}+576x^{-5}-72x^{-4}$$

Answer

$$-24x^{-4}+48x^{-3}-12x^{-2}$$

Question 5

Given $$g\left(x\right)=\frac{3}{x^2}-\frac{5}{x^4}+\frac{2}{x}$$ find $$g^{$$

Accepted Answer

$$-72x^{-5}+600x^{-7}-12x^{-4}$$

Answer

$$-6x^{-3}+20x^{-5}-2x^{-2}$$

Answer

$$18x^{-4}-100x^{-6}+4x^{-3}$$

Answer

$$360x^{-6}-4200x^{-8}+48x^{-5}$$

Question 6

Given $$g\left(x\right)=\frac{1}{9x^5}+\frac{2}{3x^4}-\frac{1}{x}$$ find $$g^{$$

Accepted Answer

$$\frac{10}{3x^7}+\frac{40}{3x^6}-\frac{2}{x^3}$$

Answer

$$\frac{3}{4x^7}-\frac{2}{5x^4}+\frac{1}{x^2}$$

Answer

$$\frac{2}{3x^4}-\frac{1}{2x^3}+\frac{5}{6x^2}$$

Answer

$$-\frac{5}{9x^6}-\frac{8}{3x^5}+\frac{1}{x^2}$$

Question 7

The second derivative to the position function is?

Accepted Answer

Acceleration

Answer

Jerk

Answer

Position

Answer

Velocity

Question 8

The first derivative to the position function is?

Accepted Answer

Velocity

Answer

Position

Answer

Acceleration

Answer

Jerk

Question 9

Find $$h^{$$ if $$h\left(x\right)=\frac{5}{\left(9x+4\right)}+\frac{4}{\left(3x+2\right)}$$

Accepted Answer

$$\frac{810}{\left(9x+4\right)^2}+\frac{72}{\left(3x+2\right)^3}$$

Answer

$$\frac{9}{\left(9x+4\right)^3}-\frac{12}{\left(3x+2\right)^5}$$

Answer

$$5\left(9x+4\right)^{-1}+4\left(3x+2\right)^{-1}$$

Answer

$$\frac{-45}{\left(9x+4\right)^2}-\frac{12}{\left(3x+2\right)^2}$$

Question 10

A particle moves along a line so that its position at any time $$t\ge0$$ is given by the function $$s\left(t\right)=\frac{1}{3}t^3-3t^2+8t-5$$ , where s is measured in meters and t is measured in seconds. Find the instantaneous velocity at any time t.

Accepted Answer

$$v\left(t\right)=t^2-6t+8$$

Answer

$$v\left(t\right)=2t-6$$

Answer

$$v\left(t\right)=2$$

Answer

$$v\left(t\right)=0$$

Question 11

A particle moves along a line so that its position at any time $$t\ge0$$ is given by the function $$s\left(t\right)=\frac{1}{3}t^3-3t^2+8t-5$$ , where s is measured in meters and t is measured in seconds. Find the acceleration at any time t.

Accepted Answer

$$v\left(t\right)=2t-6$$

Answer

$$v\left(t\right)=t^2-6t+8$$

Answer

$$v\left(t\right)=2$$

Answer

$$v\left(t\right)=0$$

Question 12

A particle moves along a line so that its position at any time $$t\ge0$$ is given by the function $$s\left(t\right)=\frac{1}{3}t^3-3t^2+8t-5$$ , where s is measured in meters and t is measured in seconds. At what time(s) is the particle at rest?

Accepted Answer

At 2 and 4 seconds

Answer

At 4 seconds

Answer

At 2 seconds

Answer

At 1 and 2 seconds

Question 13

A ball is dropped off a 1,200 ft cliff. The height of the ball over time is modeled by the function $$h\left(t\right)=1200-16t^2$$ , where h is the height in feet and t is the time measured in seconds. Find $$h$$

Accepted Answer

h'(3) = -96

Answer

h'(3) = 1200

Answer

h'(3) = -32

Answer

h'(3) = -16

Question 14

A rock thrown vertically upward from the surface of the moon at a velocity of 32 meters per second reaches a height of $$s\left(t\right)=32t-0.8t^2$$ meters in t seconds. Find the rock's velocity as functions of time.

Accepted Answer

$$v\left(t\right)=32-1.6t$$

Answer

$$v\left(t\right)=0$$

Answer

$$v\left(t\right)=32$$

Answer

$$v\left(t\right)=-1.6$$

Question 15

A rock thrown vertically upward from the surface of the moon at a velocity of 32 meters per second reaches a height of $$s\left(t\right)=32t-0.8t^2$$ meters in t seconds. Find the rock's acceleration as functions of time.

Accepted Answer

$$v\left(t\right)=-1.6$$

Answer

$$v\left(t\right)=0$$

Answer

$$v\left(t\right)=32$$

Answer

$$v\left(t\right)=32-1.6t$$

Question 16

A rock thrown vertically upward from the surface of the moon at a velocity of 32 meters per second reaches a height of $$s\left(t\right)=32t-0.8t^2$$ meters in t seconds. How long did it take the rock the reach its maximum point?

Accepted Answer

20 seconds

Answer

10 seconds

Answer

15 seconds

Answer

2 seconds

Question 17

Suppose $$h\left(x\right)=x^{\frac{5}{2}}-x^{\frac{3}{2}}$$ . What is $$h^{$$ ?

Accepted Answer

$$\frac{15}{4}x^{\frac{1}{2}}-\frac{3}{4}x^{\frac{-1}{2}}$$

Answer

$$\frac{-15}{16}x^{\frac{-3}{2}}-\frac{9}{16}x^{\frac{-5}{2}}$$

Answer

$$\frac{5}{2}x^{\frac{3}{2}}-\frac{3}{2}x^{\frac{1}{2}}$$

Answer

$$\frac{15}{8}x^{\frac{-1}{2}}+\frac{3}{8}x^{\frac{-3}{2}}$$

Question 18

If $$g\left(x\right)=\left(2x^5+1\right)\left(x^3+1\right)$$ find $$g^4\left(x\right)$$

Accepted Answer

$$3360x^4+240x$$

Answer

$$16x^7+10x^4+3x^2$$

Answer

$$112x^6+40x^3+6x$$

Answer

$$672x^5+120x^2+6$$

Question 19

Find $$f^{$$ if $$f\left(x\right)=\left(5x^3-x^2\right)\left(3x^4-7\right)$$

Accepted Answer

$$630x^5-90x^4-210x+14$$

Answer

$$3150x^4-360x^3-210$$

Answer

$$105x^6-18x^5-105x^2+14x$$

Answer

$$12600x^3-1080x^2$$

Question 20

Find $$f^{$$ if $$f\left(x\right)=\cos x+x^2-2x$$

Accepted Answer

$$\sin x$$

Answer

$$-\sin x+2x-2$$

Answer

$$-\cos x+2$$

Answer

$$-\cos x$$

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