# Answer to Question #18716 in Calculus for hsd

Question #18716

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 (separate by commas): x=

Expert's answer

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

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

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