# Thread: differentiation and several other questions

1. ## differentiation and several other questions

I don't understand how to do differentiation or to find the equation of the line tangent to the graph at the point. Could someone please help me with a few homework questions I have?

Consider the following:
Use the power rule for differentiation to find f '(x). Give your answer using the form below where B > D > F.
f '(x) = Ax^B + Cx^D + Ex^F

The next question is Find the equation of the line that is tangent to the graph of f(x) = 2x^4 - 7x^2 + 230 at the point (3, 329).
y(x)=?

Consider the following: f(x) = 3x^2 - 7x Find f(7)...I thought you would just put 7 in where x is but that answer did not work

I would appreciate any help!

2. Hello bullyluver2009

Welcome to Math Help Forum!
Originally Posted by bullyluver2009
I don't understand how to do differentiation or to find the equation of the line tangent to the graph at the point. Could someone please help me with a few homework questions I have?

Consider the following:
Use the power rule for differentiation to find f '(x). Give your answer using the form below where B > D > F.
f '(x) = Ax^B + Cx^D + Ex^F

The next question is Find the equation of the line that is tangent to the graph of f(x) = 2x^4 - 7x^2 + 230 at the point (3, 329).
y(x)=?

Consider the following: f(x) = 3x^2 - 7x Find f(7)...I thought you would just put 7 in where x is but that answer did not work

I would appreciate any help!
Although it may not seem like it, these are really very basic questions on differentiation, so you need to review any notes and examples that you've been given.

The basic rule is:
If $f(x) = ax^n$, then $f'(x) = nax^{n-1}$
In other words:
Multiply by the power, and then decrease the power by $1$.
This applies to fractional as well as integer powers, so, for example:
$f(x) = 4x^{\frac45} \Rightarrow f'(x) = \frac{16x^{-\frac15}}{5}$
Maybe you will also need to review the meaning of fractional powers; for example, $\sqrt x = x^{\frac12}$. So $f(x) = \sqrt x \Rightarrow f'(x) = \frac{1}{2\sqrt x}$.

3. Originally Posted by bullyluver2009
The next question is Find the equation of the line that is tangent to the graph of f(x) = 2x^4 - 7x^2 + 230 at the point (3, 329).
y(x)=?
If the slope of a line is m and $(x_1,y_1)$ is a point on the line, then the point-slope equation of the line is
$y-y_1=m(x-x_1)$
The derivative is the slope of the tangent line so
$m=f '(3)$
(3, 329) is a point on the tangent line so you have enough information to write its equation.

4. Originally Posted by bullyluver2009
Consider the following: f(x) = 3x^2 - 7x Find f(7)...I thought you would just put 7 in where x is but that answer did not work
Is it asking for f(7) or f'(7)?