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I actually need help with several problems

1) If f(x)=4x^2-4 x+3, then f'(5) = 36

Use this to find the equation of the tangent line to the parabola y=4x^2-4x+3 at the point (5,83). The equation of this tangent line can be written in the form y = mx+b where

m= ?

and

b= ?

2)For what values of x does the graph of f(x)=6x^3-9x^2-216x+18 have a horizontal tangent?

3)f(x) = x^{8}h(x)

h(-1) = 5

h'(-1) = 8

I need to calculate f'(-1)

4) A particle moves along a straight line with equation of motion s=t^{3}-3t^{2} Find the value of t (other than 0 ) at which the acceleration is equal to zero.

5) A particle moves along a straight line and its position at time t is given by s(t)=2t^3-15t^2+24t where s is measured in feet and t in seconds.

Find the velocity (in ft/sec) of the particle at time t=0

The particle stops moving (i.e. is in a rest) twice, once when t=A and again when t=B where A < B

A=?

B=?

What is the position of the particle at time 10?

What is the TOTAL distance the particle travels between time 0 and time 10?

Thank you,

Neil

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# Several Derivative Problems

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