1)Give the slope of the tangent line to the graph of f(x)= x^3 +2x^2 -7x -1 at t

Question

1)Give the slope of the tangent line to the graph of f(x)= x^3 +2x^2 -7x -1 at the pint where x=2.

2)Give the slope of the normal line to the graph of f(x)= x^3 +2x^2 -7x -1 at the point where x=2.

3)Give the derivative of (2x-3)/(x^2 -1) at x=2.

4)Give the value of x where the function f(x)=(x^2 +1)/x has a horizontal tangent line.

5)Let f(x)=(1/3)x^3 +2x. Give the value of x where the tangent line has slope of 3.

6)Differentiate y= 3x/(x^2 +1)

7)f(x)=x^3 -5x+47; find f ''(2).

8)Find f ''(x) (the second derivative) if f(x)=(x^2 -3x)/x^2.

9)g(x)=x^3 f(x). Find g '(2), given that f(2)=6 and f '(2)=3.

10)f(x)= x*g(x) + x/(g(x)). Given that g(2)=9, and g '(2)=18, find f '(2)=.

Explanation / Answer

1. and .2 : slope = 13
3. deivative = 2/9
4. and 5   horizontal tangent line at x= 1 , -1
6. y' = 3-3x^2/(1+x^2)^2
7. y''(2) = 12
8. y'' = -6/x^3
9. 96
10. 134/3

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