slope = m = dy/dx = 270 x^2 -15 x^4
where is m max?
dm/dx = 0 for max or min
dm/dx = 540 x - 60 x^3 = 0
x (540 - 60x^2) = 0
x = 0 or x = +/- 3
max or min at x = 0
d^2m/dx^2 = 540 - 180 x^2
that is + if x = 0, thus minium
if x = +3 that is - for x = +or - 3 so maximums there
which is bigger?
540(-3)-60(-3)^3 = 0
540(+3)-60(3)^3 = 0
so equal maximum slopes at + and - 3
At what value(s) of x on the curve y=−8+90x^3−3x^5 does the tangent line have the largest slope?
1 answer