SOLUTION: Let ƒ(x)=e−(x+1)2. Draw a graph of the function on the interval [-3,3] and estimate from the graph whether ƒ′(−1) is positive or negative or zero, and whether

Algebra ->  Test -> SOLUTION: Let ƒ(x)=e−(x+1)2. Draw a graph of the function on the interval [-3,3] and estimate from the graph whether ƒ′(−1) is positive or negative or zero, and whether       Log On


   



Question 1049842: Let ƒ(x)=e−(x+1)2.
Draw a graph of the function on the interval [-3,3] and estimate from the graph whether ƒ′(−1) is positive or negative or zero, and whether ƒ′′(−1) is positive, negative or zero.

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
f` is
e%5E%28-x%5E2-2x-1%29%2A%28-2x-2%29
from the graph
     .
f`(-1)=1
f``(-1)=2
solution

first deriv=e%5E%28-x%5E2-2x-1%29%2A%28-2x-2%29 at x=-1
first deriv=e%5E%28-1%2B2-1%29%2A%282-2%29 at x=-1
first deriv=e%5E%280%29%2A%280%29 at x=-1
first derivative is 1 at x=-1





second derivative=e%5E%28-x%5E2-2x-1%29%2A%28-2x-2%29 at x=-1
second derivative=

xat x=-1
second deriv=e%5E%28-1%2B2-1%29%2A%282-2%29%2A%282-2%29%2Be%5E%28-1%2B2-1%29%2A%282-2%29%2A%28-2%29
second deriv=e%5E%280%29%2A%280%29%2A%280%29%2Be%5E%280%29%2A%280%29%2A%28-2%29
second deriv=e%5E%280%29%2Be%5E%280%29
second deriv is 2 at x=-1