Suppose I’m thinking of a function f(x) and I know that the slope of its graph at the point (x,f(x)) is given by e^(-4x). Suppose I also know that f(1)=e^-4. Find the formula for the function.

1 answer

so you know that f'(x) = e^(-4x)
That means that
f(x) = -1/4 e^(-4x) + C
since f(1) = e^-4,
-1/4 e^-4 + C = e^-4
C = 5/4 e^-4
and so
f(x) = -1/4 e^(-4x) + 5/4 e^-4
Similar Questions
    1. answers icon 0 answers
  1. 8 of 248 of 24 Items42:23 Skip to resourcesFeature Graph of a Linear Function Consider the function: y = 8 − 2x. Question 1
    1. answers icon 1 answer
  2. 7 of 177 of 17 Items01:57:30 Skip to resourcesFeature Graph of a Linear Function Consider the function: y = 8 − 2x. Question 1
    1. answers icon 1 answer
  3. 7 of 177 of 17 Items01:59:31 Skip to resourcesFeature Graph of a Linear Function Consider the function: y = 8 − 2x. Question 1
    1. answers icon 1 answer
more similar questions