calculus
posted by victoria on .
let f be the function given by f(x)=(3x^3/e^x). for what value of x is the slope of the line tangent to f equal to 1.024?
a)9.004
b)4.734
c)1.029
d)1.277
e)4.797

just differentiate and solve. What's the trouble?
f = 3x^3*e^x
f' = (9x^2  3x^3)e^x
= 3x^2(3x)e^x
Now, x^2 >= 0 and e^x >= 0
so the only way we can have f' < 0 is x>3
That means choice (e)
Check: 3*4.797^2*(34.797)e^4.797 = 1.024