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?
In this equation, "k" represents a constant or a coefficient that is being multiplied by -1/2. It is a variable that can take on different values depending on the context of the problem.
To solve for "k" in this equation, you can use basic algebraic principles. First, isolate the variable by getting it on one side of the equation. Then, perform the inverse operation on both sides of the equation to isolate "k" on its own. Finally, check your answer by plugging it back into the original equation.
Yes, the value of "k" can be negative in this equation. Since it is being multiplied by a negative number (-1/2), the overall result can be either positive or negative depending on the value of "k".
There are infinitely many possible solutions for "k" in this equation, as any real number can be plugged in for "k" and the equation will still hold true. Some commonly used values for "k" include integers, fractions, and decimals.
Solving for "k" is a fundamental concept in algebra and can be applied in many real-life scenarios. For example, it can be used to find the unknown interest rate in a loan or the missing coefficient in a chemical reaction. It is also widely used in solving equations and inequalities in various fields of science and engineering.