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Calc 1 2.3

 

<== Calculus 1
Number Question Answer
See the work

1.

 

If ƒ(x)=2x^2-9x-23, find ƒ'(x)  

 

ƒ'(x)= 4x-9

 

The work

Point Cost: 2

 

2.

 

If ƒ(x)=sqrt(2), find ƒ'(x)

 

ƒ'(x)= 0

 

The work

Point Cost: 1

 

3.

 

 

Let ƒ(x)=4x^8-6x^5-6x^3+4x.

Find ƒ'(x)

Find ƒ'(1) 

 

ƒ'(x)= 32x^7-30x^4-18x^2+4    

ƒ'(1)= -12

 

The work

Point Cost: 3

 

4.

 

If ƒ(t)= 6sin(t)-2πcos(t), find ƒ'(t)       

 

6cos(t)+2πsin(t)

 

The work

Point Cost: 3

 

5.

 

If

ƒ(t)= sqrt(5)/(t^5)

FInd ƒ'(t)

Find ƒ'(2)

 

ƒ'(t)= (-5)(sqrt(5))/t^(6)

ƒ'(2)=-0.174692810742171

 

The work

Point Cost: 3

6.

 

If ƒ(x)=4+(4/x)+(6/x^2), find ƒ'(x)

 

-4x^(-2)-12x^(-3)

 

The work

Point Cost: 3

 

7.

 

 

Let ƒ(x)= -5x(x-2).
Then ƒ'(-3)=_____.
And after simplifying ƒ'(x)=______

 

ƒ'(-3)= 40

ƒ'(x)= -10x-9

 

The work

Point Cost: 3

 

8.

 

If ƒ(x)=(x-5)(4x+1), then ƒ'(x)=____

 

8x-19

 

The work

Point Cost: 3

 

9.

 

 

 

If ƒ(x)=2sqrt(x)(x^3-7sqrt(x)+3

Find ƒ'(x)=_____

Find ƒ'(3)=_____

 

f'(x)= ƒ'(x)= 7x^2.5-14+3x^(-.5)

ƒ'(3)= 96.8512516844082

 

The work

Point Cost: 3

 

10.

 

If y=5π^2, find y'

 

0

 

The work

Point Cost: 1

 

11.

 

If ƒ(u)=sqrt(2)u+sqrt(4u), find ƒ'(u)

 

sqrt(2)+1/(sqrt(u))

 

The work

Point Cost: 3

 

12.

 

If ƒ(x)=(2x^2+12x+31)/sqrt(x), find ƒ'(x)   

 

ƒ(x)= (2)*(3/2)*(x^(1/2)) + (12/2)*(x^(-1/2)) -(31/2)*(x^(-3/2))         

 

The work

Point Cost: 3

 

13.

 

If ƒ(x)=(2x^5+2x^4+4x^3)/(x^4), find ƒ'(x)    

 

ƒ'(x)=2-4/x^2

 

The work

Point Cost: 3

 

14.

 

 

If ƒ(t)= (sin(t)/4)+(3/t), then

ƒ'(t)=______

 

ƒ'(t)= (cos(t)/4)-(3/t^2)

 

The work

Point Cost: 3

 

15.

 

If ƒ(t)= (t^2)^(1/3)+2(sqrt(t^3)), find ƒ'(t)

 

ƒ'(t)=(2/3)*(t^(-1/3))+(3)*(t^(1/2))

 

The work

Point Cost: 3

 

16.

 

 

 

Find the equation of the tangent line to the
curve y=6sinx at the point (π/6,3). Compute
m and b.
m=____
b=_____

 

m= 6*sqrt(3)/2
b= 3-(6*sqrt(3)/2*π/6)

 

The work

Point Cost: 3

17.

 

 

Find the equation of the tangent line and normal
line to the curve y=(2+4x)^2 at the point (6,676).
Tangent line: y=____
Normal line: y=_____

 

Tangent line: y=208*(x-6)+676
Normal line:
y= -(x-6)/208 + 676

 

The work

Point Cost: 3

 

18.

 

 

Find the first and second derivative of the function.
ƒ(x)= 6sinx+10cosx
ƒ'(x)=______
ƒ''(x)=______

 

ƒ'(x)= 6*cos(x)-10*sin(x)
ƒ''(x)= -6*sin(x)-10*cos(x)

 

The work

Point Cost: 3

 

19.

 

 

 

Find the points on the graph of f(x)= 2x^3+9x2-168x+14
where the tangent is horizontal. List the x-values of
these points.
x value(s)=_______

 

x value(s)= -7, 4

 

The work

Point Cost: 3

20.

 

If a ball is thrown vertically upward from the roof
of 64 foot building with a velocity of 48 ft/sec, its
height after t seconds is s(t) = 64+48t-16t^2.

a.) What is the maximum height the ball reaches?
Answer:_______

b.) What is the velocity of the ball when it hits
the ground?
Answer:_______

 

a) 100 ft


b) -80

The work

Point Cost: 4