1. ## Derivatives Help!

1)Find the slope of the tangent line to the graph at any point
f(x)=sqrt (3-x)

2) Find the slope of the tangetn line to the graph at given point and give an equation of the tangent line
f(x)=3/2x at (1, 3/2)

3)Let f(x)=x^2+6x
a) Find the derivative f' of f
b) Find the point on the graph of f where the tangent line to the curve is horizontal
hint: find the value of x for which f'(x) =0

I'm having problems with derivatives, can anyone teach me how to do these problems step by step! I appreciate it!

2. Originally Posted by lemontea
1)Find the slope of the tangent line to the graph at any point
f(x)=sqrt (3-x)

2) Find the slope of the tangetn line to the graph at given point and give an equation of the tangent line
f(x)=3/2x at (1, 3/2)

3)Let f(x)=x^2+6x
a) Find the derivative f' of f
b) Find the point on the graph of f where the tangent line to the curve is horizontal
hint: find the value of x for which f'(x) =0

I'm having problems with derivatives, can anyone teach me how to do these problems step by step! I appreciate it!
use the formula

$yf(x_0)=f'(x_0)(x-x_0)$

where $f'(x)=\lim_{\Delta{x}\to{0}}\frac{f(x+\Delta{x})-f(x)}{\Delta{x}}$

or the derivative

3. Originally Posted by lemontea
1)Find the slope of the tangent line to the graph at any point
f(x)=sqrt (3-x)

2) Find the slope of the tangetn line to the graph at given point and give an equation of the tangent line
f(x)=3/2x at (1, 3/2)

3)Let f(x)=x^2+6x
a) Find the derivative f' of f
b) Find the point on the graph of f where the tangent line to the curve is horizontal
hint: find the value of x for which f'(x) =0

I'm having problems with derivatives, can anyone teach me how to do these problems step by step! I appreciate it!
1) chain rule:
sqrt (3-x) = (3-x)^(1/2)
f'(x)=1/2*(3-x)^(-1/2)*(-1)=1/(2(3-x)^(1/2))

2)is that a 3/(2x) or (3/2)x?

3a)2x+6
b)2x+6=0, x=-6/2=-3