1. Consider the function f(x)=( 3x-1 )^3 (5x+1) The whole function is in bracket

Question

1.

Consider the function f(x)=(3x-1)^3

                                           (5x+1)

The whole function is in brackets to the 3rd power.

Please show work for the first derivative of x.

Also need to find the equation of the tangent line at x=0

2.

The altitude in feet of a vertically launched rocket t seconds after launch from the roof of a building is given by

h(t) = 1/12t^4-2/3t^3+4t^2+8+5 where 0<or equal to t<or equal to 8. Find the acceleration, the velocity and the altitude of the rocket 3 seconds after launch.

Thank you. Please show work so I can follow.

Explanation / Answer

1)

f(x)= ((3x+1)(5x+1))^3

derivative :

6*((1-3x)^2)*((5x+1)^2)*(15x-1)

equation of tangent :

y=24x+1

2)

i guess u typed it wrong

i am taking h(t) as h(t) = 1/12t^4-2/3t^3+4t^2+8t+5

acceleration : 5 feet/sec^2

velocity : 23 feet/sec

altitude : 53.75 feet

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