find dy/dx

Question

1. find dy/dx for y= 1/3x^3 +x^7/10

 

2. find the values of x where the tangent line is horizontal for f(x)=3x^3-2x^2-9

 

3. find the derivative of y=3x^5-7x^2-4/x^2 

 

4.f(x)= lim h_0 f(x+h)-f(x)/h

 

Answer 1

Not sure what the values are in #1

 

#2 take the derivative and solve when it is zero.  horizontal tangent lines occur at zero values of the derivative

 

f' = 9x² - 4x

 

0 = x(9x - 4)

 

set the factors to zero and solve for x

 

x = 0

 

(9x -4) =0

9x = 4

x = 4/9

 

so the potential horizontal tangent lines are at x = 0 and x = 4/9

 

#3  not sure how to interpet the function  (is x² a denominator for the whole expression or just a term)  I will treat it as it is the entire expression and use the quotient rule

 

y' =  (x² (15x⁴ - 14x) - 2x(3x⁵ - 7x² -4))/x⁴

 

#4

 

i think some info may be missing