In this post, we will be discussing the slope of a tangent line. We will first find the equation for the tangent line and then determine where it has the largest slope. The equation for a tangent line is y = mx + b. To find its slope, we need to use calculus and take derivatives of both sides of the equation: d(y)/dx = 3×5 − 40×3 + 6b − d(mx)/dy = 5×4 − 80×2 + 4b It can then be determined that at which points on the curve y = 1+40*(1/3)^3−3*(1/5)^5 does .. Problem: the sentence is not grammatical Solution: at which points on the curve y = ƒ(x) does the tangent line have a slope of m. This becomes, “at which points on” and then continues with “the curve” and then has an incomplete thought. The last word should be either “.. do we find”. It is also worth noting that there are unnecessary words like ‘which’ in this sentence. (Though they may seem necessary when reading it through quickly.) It can then be determined that at what point .. or simply, At what point..does the tangent line have a slope of m? Where along this equation does its slope equal or become greater than -m/b”?