Answer to Question #18716 in Calculus for hsd

Question

At what value(s) of x on the curve y=10+250x3−3x5 does the tangent line have the largest slope?

Answer (separate by commas): x=

Answer 1

tangent line slope is maximum where the derivative hasmaximum.

The derivative is
y' = 250*3x^2-3*5x^4=750x^2-15x^4.
y' has 2 maximums - at +(50)^{1/4} and at -(50)^{-1/4}.
at this 2 points tangent line slope to y is the biggest