Finding k when the curve y=−2kx³+4kx has slope 25 at x=3

[caters]

Homework Statement

If the slope of the curve y=−2kx^3+4kx at x=3 is 25, what is the value of k?

Homework Equations

f(x)=xⁿ
f'(x)=nx^n-1

The Attempt at a Solution

y=f(x)

f(x)=-2kx³+4kx
f'(x)=-6kx²+4k
x=3
f'(3)=-50k

-50k = 25
-k=1/2
k=-1/2

Did I do it right?

 

[Dick]

Homework Statement

If the slope of the curve y=−2kx^3+4kx at x=3 is 25, what is the value of k?

Homework Equations

f(x)=xⁿ
f'(x)=nx^n-1

The Attempt at a Solution

y=f(x)

f(x)=-2kx³+4kx
f'(x)=-6kx²+4k
x=3
f'(3)=-50k

-50k = 25
-k=1/2
k=-1/2

Did I do it right?

Yes.