1. The problem is to find the value of $x$ where the slope of the tangent to a curve is given or needs to be determined. 2. The slope of the tangent line to a curve at a point is given by the derivative of the function at that point. If the function is $y=f(x)$, then the slope of the tangent at $x$ is $f'(x)$. 3. To find $x$ for a specific slope $m$, set the derivative equal to $m$: $$f'(x) = m$$ 4. Solve this equation for $x$. This may involve algebraic manipulation, factoring, or using inverse functions depending on $f'(x)$. 5. Example: If $f(x) = x^2$, then $f'(x) = 2x$. To find $x$ where slope is 4, solve $2x=4$ which gives $x=2$. 6. In summary, find the derivative $f'(x)$, set it equal to the desired slope, and solve for $x$.