Thread: derivative

Please help me with the circled qns (ii) and qn (a) and (b)

see if you can get the paper's answer: (ii): -0.962
qn (a) -13/9 < k<3
(b) a=1,b=-10

if u can pls tell me yr workings

II

I agree with the Paper's answer. It seems to me that it would be very difficult to get the integral wrong if you managed to partial frations correctly. What did you get for the partial fraction decomposition?

2 - x + what/(x+5) - what/(x-5)

a

Get everything on the left side and look at it. Gather like terms until it looks like a quadratic. What happens when the discriminant is less than zero?

b

You have x = 2.

From the line, you can determine the coordinates of the point of tangency. Substitute x = 2 and y = ????? into the cubic.

From the slope of the line, you can determine the value of the first derivative of the cubic. Substitute x = 2 into the derivative and y`(2) = the slope of the line.

You may have a little algebra after that.

Those are the workings.

(ii) i got the correct answer for the partial fraction as stated in the paper...but when i integrate it i got a different answer..
i got -x +2 + 3/10(1/5+x) + 3/10(1/5-x) as the partial fraction

and when u integrate 3/10(1/5+x) dx, is it equal to 3/10[1n(5+x)]4,1 ?? P.S 4,1 is supposed to be beside top n bottom of the [] bracket

(a) why is it dat the discriminant is less than zero?

(b)From the slope of the line, you can determine the value of the first derivative of the cubic. wat do u mean by this? wad is the first derivative?

i got -x +2 + 3/10(1/5+x) + 3/10(1/5-x) as the partial fraction

Get a little better at the notation. It's okay for now, because I already know what you mean. "3/10(1/5+x)" this is bad. You mean (3/10)*(1/(5+x)) - a couple extra parentheses clear it up.

and when u integrate 3/10(1/5+x) dx, is it equal to 3/10[1n(5+x)]4,1 ?? P.S 4,1 is supposed to be beside top n bottom of the [] bracket

Okay, but I must wonder if you got the last one. [int 1/(5-x) dx] is NOT ln(5-x) + C. You tell me what is wrong with it.

(a) why is it dat the discriminant is less than zero?

What do you remember about quadratic equations? It means, "No Real Solutions". Why is that helpful?

(b)From the slope of the line, you can determine the value of the first derivative of the cubic. wat do u mean by this? wad is the first derivative?

Now we have a problem. If you have integral problems, you should already be familiar with derivative problems.

f(x) = ax^3 + b*x

f`(x) = 3ax^2 + b

Ringing any bells?