Question

Sketch the graph of a function whose first derivative is always negative and second derivative is always positive.

Answer 1

Y = f(x)
y' < 0 
y'' > 0

Function must be decreasing and concave

$f(x)= e^{-x} \\ \\f'(x)=- e^{-x}\ \textless \ 0=-\frac{1}{e^x} \ \textless \ 0 \\ \\f''(x)=(-e^{-x})'=e^{-x}= \frac{1}{e^x} \ \textgreater \ 0$