Question

At which point on the following curve does the tangent line has the largest slope?

𝑦 = 1 + 40𝑥^3 − 3𝑥^5

Answer 1

$y'\left( x \right) \rightarrow \max \\y'=120x^2-15x^4\rightarrow \max \\{x^2}_{\max}=\frac{-120}{2\cdot \left( -15 \right)}=4\\x=\pm 2$