1.
a) If y=f(x)=x<sup>2</sup>-6x+7, find f'(a)
I got : f'(a)=2a-6, but I wasn't sure because it just seemed to easy.
b)The limit as h approaches 0((2+h)<sup>3</sup>-8)/h represents the derivative of some f(x) at some point a. Find f(x) and a.
I wasn't sure how to go about this one, but I'm sure once I start it won't be too hard.
2. Use the graph of y=f(x) below to estimate the value of each derivative, and then sketch the graph of the derivative function.
a)f'(0)
b)f'(1)
c)f'(2)
d)f'(3)
I can't post the graph here, but I'm not sure how to go about doing this one either....
3. Consider the function shown in problem #2 to be f'(x), then use this f'(x) to sketch f(x).
I'd need to do number two to do this one.
4. Find f'(x) if f(x)=x<sup>3</sup>-x<sup>2</sup>-2x+10
I got : f'(x)=3x<sup>2</sup>-2x-2
5. I can't post this one because it's all about a graph, but what does f"(x) mean?
6. For the function y=f(x)=x<sup>3</sup>-3x<sup>2</sup>-x+3
a) Find the critical values. (what are critical values? I didn't understand the definition in the text book.
b) For what values of x is the function increasing?
I got : -2<x<0, x>or=3
c) For what values of x is the function decreasing?
I got : 0<x<2
d) For what values of x is the function concave up?
I don't understand this question.
7. I can't post this either because it has to do with a graph, but if I can figure out number 6, then I can do this one.
8. Find the linear approximation of y=f(x)=1/(2x) at a=3
a) If y=f(x)=x<sup>2</sup>-6x+7, find f'(a)
I got : f'(a)=2a-6, but I wasn't sure because it just seemed to easy.
b)The limit as h approaches 0((2+h)<sup>3</sup>-8)/h represents the derivative of some f(x) at some point a. Find f(x) and a.
I wasn't sure how to go about this one, but I'm sure once I start it won't be too hard.
2. Use the graph of y=f(x) below to estimate the value of each derivative, and then sketch the graph of the derivative function.
a)f'(0)
b)f'(1)
c)f'(2)
d)f'(3)
I can't post the graph here, but I'm not sure how to go about doing this one either....
3. Consider the function shown in problem #2 to be f'(x), then use this f'(x) to sketch f(x).
I'd need to do number two to do this one.
4. Find f'(x) if f(x)=x<sup>3</sup>-x<sup>2</sup>-2x+10
I got : f'(x)=3x<sup>2</sup>-2x-2
5. I can't post this one because it's all about a graph, but what does f"(x) mean?
6. For the function y=f(x)=x<sup>3</sup>-3x<sup>2</sup>-x+3
a) Find the critical values. (what are critical values? I didn't understand the definition in the text book.
b) For what values of x is the function increasing?
I got : -2<x<0, x>or=3
c) For what values of x is the function decreasing?
I got : 0<x<2
d) For what values of x is the function concave up?
I don't understand this question.
7. I can't post this either because it has to do with a graph, but if I can figure out number 6, then I can do this one.
8. Find the linear approximation of y=f(x)=1/(2x) at a=3