Originally Posted by

**ghostanime2001** Hi I've been stuck with this question for quite a while. School's been over for a week and I have been trying to solve this problem over and over and over again and I failed to get the answers to these following questions. If anybody who can help me please do help I'm sure somebody out there will benefit from my response as well.

1. Let P(a,b) be a point on the curve √x + √y = 1. Show that the slope of the tangent at P is

-√b

------

√a

Mr F says: Are you familiar with implicit differentiation?

2. For the power functions f(x) = x^n, find the x-intercept of the tangent to its graph at point (1,1). What happens to the x-intercept as n increases without bound (n --> +OO (positive infinity) ) ? Explain the result geometrically

Mr F says: Where are you stuck? $\displaystyle {\color{red} f'(x) = n x^{n-1} \Rightarrow m = n \, \text{at} \, x = 1}$. Then the equation of the tangent is $\displaystyle {\color{red} y - 1 = n(x - 1) \Rightarrow y = ......}$.

3. For each function, sketch the graph of y=f(x) and find an expresssion for f ' (x). Indicate any points at which the f ' (x) does not exist.

a) f(x) = [ x^2, x < 3

[ x + 6, x >-(x is greater or equal then 3) 3 ]

b) f(x) = I3x^2 - 6I I means absolute value bars

c) f(x) = I IxI - 1 I I means absolute value bars

That is all. I'd greatly appreciate it. Thanks.