f(x)= 3+4xe^{-5x}complete the sentences concerning the function

Question

a) the function f is decresing on the iterval......

b) the function f is increacing on the interval

c) the function f is concave down on the interval

d) the function f is concave up on the interva

Answer 1

f is decreasing when f' is negative
and similarly for increasing
f is concave down when f" is negative
and similarly for concave up

f = 3 + 4xe^-5x
f' = 4(1-5x)e^-5x
f" = 20(5x-2)e^-5x

Hint: e^-5x is never zero