1. ## random calculus questions

i worked it out by differentiating f(y) and then g(y) to get:

5Ay^-6 + Be^y

but that's not hte right answer. am i differentiating wrong?

Find the equations of the tangent line, y1, and the normal line, y2 to the following curve at the given point P.

for y1 i got the derivative of y to get 4x^3 + 9e^x
and for y2 it should be the same thing since x is 0, i'm not sure what i'm doing wrong since both my answers are incorrect

Find a second-degree polynomial P such that the following conditions are met. P (6) = 8
P ' (6) = 8
P '' (6) = 4

this one is puzzling me as i'm not sure whre to start, should i start w/ functions that will work for original or should i start at the p"? not sure

2. Originally Posted by deltemis

i worked it out by differentiating f(y) and then g(y) to get:

5Ay^-6 + Be^y

but that's not hte right answer. am i differentiating wrong?
It would help if you say what you are supposed to do, but lets assume you are asked to differentiate $\displaystyle z$, but with respect to what? I will assume $\displaystyle y$, so:

$\displaystyle \frac{dz}{dy}=\frac{d}{dy}\left[\frac{A}{y^5}\right]+\frac{d}{dy}\left[Be^y\right]$ $\displaystyle = -\, \frac{5A}{y^6}+Be^y$

CB

3. Originally Posted by deltemis

i worked it out by differentiating f(y) and then g(y) to get:

5Ay^-6 + Be^y

but that's not hte right answer. am i differentiating wrong?
I presume that you wrote f(y) as $\displaystyle Ay^{-5}+ Be^y$ and then used the fact that the derivative of $\displaystyle y^n$ is $\displaystyle ny^{n-1}$ and the derivative of $\displaystyle e^y$ is $\displaystyle e^y$j. That would give -$\displaystyle 5Ay^{-6}+ Be^y$. Do you see the difference?

Find the equations of the tangent line, y1, and the normal line, y2 to the following curve at the given point P.

for y1 i got the derivative of y to get 4x^3 + 9e^x
and for y2 it should be the same thing since x is 0, i'm not sure what i'm doing wrong since both my answers are incorrect
Yes, that is the correct derivative but what did you then do to find the tangent line? The tangent line at (0, 9) has slope $\displaystyle 4(0^3)+ 9(e^0)= 9$ and the normal line will have slope -1/9.

Find a second-degree polynomial P such that the following conditions are met. P (6) = 8
P ' (6) = 8
P '' (6) = 4

this one is puzzling me as i'm not sure whre to start, should i start w/ functions that will work for original or should i start at the p"? not sure
Start by writing your polynomial as $\displaystyle P(x)= Ax^2+ Bx+ C$, a general second degree polynomial. Find P' and P" from that. Setting P(6)= 8, P'(6)= 8, and P''(6)= 4 will give you three equations for A, B, and C.

It might be even easier if you write the polynomial as $\displaystyle P(x)= A(x- 6)^2+ B(x- 6)+ C$ which is also a perfectly good "general second degree polynomial".