find the tangents to the curve y=2x^3+3x at the points where the slope is 9. what is the smallest slope on the curve? at what value of x does the curve have this slope? please help and show all steps!

Question

turingtest · Answer

since the geometric definition of the derivative is the slope of the tangent line of a function at some point you are being asked to solve
dy/dx=9

turingtest · Answer

actually you took the derivative wrong
y=2x^3+3x
dy/dx=6x^2+3=9
so solve that...

anonymous · Answer

oops! sometimes easy functions are hard to differentiate on the computer.

anonymous · Answer

so x = 1 and -1 but what is the smallest slope on the curve???