Question

Find the relative extrema and the points of inflection (if any exist) of the function. Use a graphing utility to graph the function and confirm your results. (If an answer does not existenter DNE.) F(x) = 7er - 7e- 2 maximum (x, y) minimum (x, y) = 10 inflection point (x, y) = (1

Answer 1

Here, we are going to find the point of maxima and minima by having the derivative test as:

Given, flx) = 7"-70" = {(exce) 2. @ Manima occurs when f'(X)=0 and f"H) <O => ['(1) - 7 led te-x) = 0 sette -d=0 >ex=-e Here f(n) is never gese line" = inlex) So, marimum : DNE -> 7 DNE 6 Minima occurs when f'(x)=0 and f'(X>0 => f'(u) = lek te-1) = 0 here fw never becomes yeso menim am point o for point of inflection f(1) = 0 zle :le"-ex=0 e"=en => x=0, here, at no, y = 0 point of infection ocurs, point 44,99 = (0,011 2 Inflection

Given, flx) = 7"-70" = {(exce) 2. @ Manima occurs when f'(X)=0 and f"H) <O => ['(1) - 7 led te-x) = 0 sette -d=0 >ex=-e Here f(n) is never gese line" = inlex) So, marimum : DNE -> 7 DNE 6 Minima occurs when f'(x)=0 and f'(X>0 => f'(u) = lek te-1) = 0 here fw never becomes yeso menim am point o for point of inflection f(1) = 0 zle :le"-ex=0 e"=en => x=0, here, at no, y = 0 point of infection ocurs, point 44,99 = (0,011 2 Inflection

Now,

We can also see from the graph that point of maxima and minimum do not exist. And an infection point exists as:

exce-" 9raph en (0,1). f'(х) = e'te-e „е“+-)