Equation of the tangent line at the indicated point

1. Oct 29, 2011

carlarae

1. The problem statement, all variables and given/known data
Find an equation of the tangent line at the indicated point on the graph of the function.
y=f(x)=x^3/4 , (x,y)=(6,54)

2. Relevant equations

3. The attempt at a solution

I did the derivative which I get 3x^2/4 and then I plugged in the 6 and get 162. Is that the whole answer? right answer? it's asking for an equation and 162 doesn't look like an equation to me.

2. Oct 29, 2011

Staff: Mentor

This is wrong. Show us how you got that number.
No and no. The question asks for the equation of the tangent line to the curve at the point (6, 54). If you know the slope m of a line and a point (x0, y0) on it, the equation of the line is y - y0 = m(x - x0).

3. Oct 29, 2011

carlarae

So is the derivative of x^3/4 not 3x^2/4? That will make a big difference for me to take another crack at this.

4. Oct 29, 2011

I like Serena

Welcome to PF, carlarae!

Hmm, if I fill in x=6 in 3x^2/4 I get a different result...

But yes, the derivative of $x^3 \over 4$ is $3x^2 \over 4$.

5. Oct 29, 2011

Staff: Mentor

Sorry I wasn't more specific. As I like Serena points out, your derivative is fine, but the value you got isn't.

6. Oct 29, 2011

HallsofIvy

Staff Emeritus
Is the function
$$\frac{x^3}{4}$$
or
$$x^{\frac{3}{4}}$$?
what you wrote was ambiguous. If the function is the first, then the derivative is
$$\frac{3}{4}x^2$$
if the second, then the derivative is
$$\frac{3}{4}x^{-1/4}= \frac{3}{4x^{1/4}}$$

7. Oct 29, 2011

Staff: Mentor

It's the first. What she wrote actually isn't ambiguous, if you allow for exponentiation being higher in precedence than multiplication or division.