`f(x) = kx^4, y = 4x - 1` Find k such that the line is tangent to the graph of the function.
The tangent line will touch one point of the original function. This means that:
`kx^4 = 4x-1`
We have two variables that we don't know.
Find the derivative of `f(x)` . The k is a constant and we can use the power rule.
`f'(x) = 4kx^3`
The slope of the tangent line is four, so we will plug that into this equation.
`4 = 4kx^3`
Divide four k on both sides.
Substitute k back into the first equation, .
`(1/x^3)x^4 = 4x-1`
`x = 4x-1`
Plug this back to to determine k.
`k(1/3)^4 = 4(1/3)-1`
Multiply 81 on both sides.
`k= 81/3 = 27`