Equation of the tangent line at the indicated point

[carlarae]

Homework Statement

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)

Homework Equations

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.

 

[Mark44]

Homework Statement

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)

Homework Equations

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.

This is wrong. Show us how you got that number.

Is that the whole answer? right answer?

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).

it's asking for an equation and 162 doesn't look like an equation to me.

 

[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.

 

[I like Serena]

Welcome to PF, 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.

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 $3x^2 \over 4$.

 

[Mark44]

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.

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

 

[HallsofIvy]

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
$$\frac{3}{4}x^{-1/4}= \frac{3}{4x^{1/4}}$$

 

[Mark44]

Is the function
$$\frac{x^3}{4}$$
or
$$x^{\frac{3}{4}}$$?
what you wrote was ambiguous.

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