Question

let f be the function given by f(x)=-2e^x^3. F0r what value of x is the slope of the line tangent to the graph of f at (x,f(x)) equal to -6

Answer 1

let f(u)=e^u
and u= x^3

f'(u)=e^u du/dx
but du/dx= 3x^2

f'(x)=e^(x^3) * 3x^2

Answer 2

so, now you just want to find where

-2*3x^2 e^x^3 = -6
x^2 e^x^3 = 1

I think a graphical solution will be easiest.