The value of k in the equation y=−2kx^3+4kx, given that the slope at x=3 is 25, is definitively -1/2. The derivative of the function, f'(x)=-6kx^2+4k, was evaluated at x=3, resulting in f'(3)=-50k. Setting -50k equal to 25 leads to the conclusion that k=-1/2. This solution is confirmed as correct by participants in the discussion.
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caters said: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)=nxn-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?