I have 3 calc problems that i have not been able to do please help me... i've been on here yesterday as well but no one was able to assist me with these particular ones...

Question

1. If f(x)=5x^3–2/x-4
find f'(x)____

what i got was (4x^2+7x-12)/x^8

2. The position function of a particle is given by s=t^3–4t^2–7t t>=0
where s is measured in meters and t in seconds. When does the particle reach a velocity of 10 m/s? ____

3. f(x)=2x^2+7x+3/ sqroot of x

Find f'(x)

i got ((x^(-1/2))(4x+7)+1/2x^(-3/2)(2x^2+7x+3))/x

Answer 1

1. If f(x)=5x^3–2/x-4
find f'(x)____
=============================
I assume you mean

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

(x-4)(15 x^2) - (5 x^3-2)(1)
----------------------------
x^2 - 8 x + 16

15 x^3 -60 x^2 - 5 x^3 +2
-------------------------
x^2 - 8 x + 16

10 x^3 -60 x^2 +2
-----------------
x^2 - 8 x + 16
what i got was (4x^2+7x-12)/x^8

2. The position function of a particle is given by s=t^3–4t^2–7t t>=0
where s is measured in meters and t in seconds. When does the particle reach a velocity of 10 m/s? ____
===========================
s' = 3 t^2 - 8 t - 7 = 7
3 t^2 - 8 t -14 = 0
t = [ 8 +/- sqrt (64 +84) ] /6
= [8 +/- 12.17]/6
=3.36
==============================

3. f(x)=2x^2+7x+3/ sqroot of x

Find f'(x)

sqrt (x) (4x+7) - (2x^2 + 7 x +3)(1/2x)sqrt x
----------------------------------------
x

2 x sqrt (x)(4x+7) - (2 x^2+7x+3) sqrt x
---------------------------------------
x

(sqrt x)[8 x^2 +14 x - 2 x^2 -7 x - 3]
--------------------------------------
x

(sqrt x/x) (6 x^2 + 7 x -3)

6 x^(3/2) + 7 x^(1/2) - 3 x^-(1/2)
======================================
i got ((x^(-1/2))(4x+7)+1/2x^(-3/2)(2x^2+7x+3))/x

Answer 2

I don't exactly know why but all of the answers were wrong.

Answer 3

2. The position function of a particle is given by s=t^3–4t^2–7t t>=0
where s is measured in meters and t in seconds. When does the particle reach a velocity of 10 m/s? ____
===========================
s' = 3 t^2 - 8 t - 7 = 10
3 t^2 - 8 t -17 = 0
t = [ 8 +/- sqrt (64 + 204) ] /6
= [8 +/- 16.4]/6
=4.94